# Acceleration Of Pulley System No Friction

Since they are attached, the blocks will be moving with the same velocity and acceleration. In fact, it is a general result that if friction on an incline is negligible, then the acceleration down the incline is a = g sin θ , regardless of mass. At the instant after the system of objects is released, find (a) the tension T in the string, (b) the acceleration of m2, (c) the acceleration of M, and (d) the acceleration of m1. Instead it is a disk of radius 0. If friction in all the pulleys is negligible, then (A) tension in thread is equal to 1/2 mg B A C (B) acceleration of pulley C is equal to g/2 (downward) (C) acceleration of pulley A is equal to g/2 (upward). and g, if there's no friction between m. k = spring constant. An example of such motion is that of a hovercraft. There is no friction and the pulley and string are massless. In order for the wagon on the table to move, the weight hanging over the side of the table must be at least…. 00 m/s 2 to the left, and the surfaces are rough. Subtract this force from the applied force to find the acceleration of the object. It is attached by a rope over a pulley to a mass of kg which hangs vertically. 0 N and M= 5. Find the acceleration and the tension in the rope of the system of masses shown (M > m), neglecting the mass of the string and the inertia of the pulley assume that the static and kinetic friction coefficients are equal to μ 1 μ 2 and the slope angle θ are known. There is no friction between block 3 and the table. The pulley starts rotating, so there is an increase in its rotational kinetic energy. Careful measurement when there is no net force allows the student to compensate for friction. The rope and the pulleys are massless and there is no friction. Using these values, and the formula for conservation of energy, it is possible to determine how much work was done by the system, in the form of friction: The other work is -2. In this section we will look at the behavior of systems that involve ropes and pulleys. After C has moved 5 m to the right, its velocity is 3 m/s. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics. This answer was originally very wrong, but it has been fixed. Note that the tension in the rope is NOT equal to the weight of the hanging mass except in the special case of zero acceleration. tension should be constant, but less than “mg”. Block, Tackle or Pulley Calculator. The axle is connected to the support. D) one-fourth of g. Which of the following is a way of maximizing the system's acceleration? You would then be given options like "maximize M and m and minimize ," or "maximize and m and minimize M. 0kg acrobat. If you are using a pulley system then there is friction between the rope and the pulley and there is also friction within the ball bearings of the. the acceleration of the system. The angle θ and the masses of the blocks m and M are given. If the component of the gravitational force down the slope is greater than the maximum frictional force, then it will slide. NB: For this problem, a coordinate system of right for A, down for m and clockwise for the pulley is adopted to be positive. In the system shown above, the block of mass Ml is on a rough horizontal table. attached by thin, very light wire wrapped around the rim of the drum (the figure ). 80 m above the ground, and the massless frictionless pulley is 4. Consider the two-body system shown below. There is no friction between block Band the ground as well as between the pulley and the ground, while the coe cient of static and kinetic friction between block Aand block. 25 m, calculate the linear acceleration of the block. The system is released from rest, and there is no friction at the axle of the pulley. A car of mass 600 kg towes a trailer of mass 250 kg in a straight line using a rigid towe-bar. Now that the acceleration has been found from Equation 5, its value can be substituted into Equation 4 in order to determine the tension. P = power. B is set into downward motion, it descends at a constant speed. This answer was originally very wrong, but it has been fixed. If you can work through and understand them you should be able to solve most standard pulley problems. Physics 211 Week 9 Rotational Dynamics: Atwood's Machine Revisited Consider a realistic Atwood's machine where the pulley is not massless. to get the coefficient of friction (note that mu has no units): 100/148 = 0. For block 1, Earth exerts a downward gravitational force F E on 1!. ) The reaction to the force the floor applies to you is the force you apply to the floor. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics. Solution: From above, we have a spring mass system modelled by the DE 2y00 +18y = 0. Set up the ramp at a relatively low angle (one that does not cause the friction block to begin sliding down the ramp by itself). Pulley has an axle around which it rotates and a string passes over the pulley. This one will be about physics, so not much groundbreaking programming algorithms. The hard way is to solve Newton's second law for each box individually, and then combine them, and you get two equations with two unknowns, you try your best to solve the algebra without losing any sins, but let's be honest, it usually goes wrong. We don’t know for sure that the system accelerates, because the force of static friction could prevent any motion. According to Newton's second law, this force produces a maximum acceleration of a = F/m = µg. Newton's second law says: Where F net is the total force an object, m is the mass and a the acceleration. Example - Pulling Force on Inclined Plane. mass m, the acceleration a that results is directly proportional to the net force and has a magnitude that is inversely proportional to the mass. A bucket with mass m 2 and a block with mass m 1 are hung on a pulley system. One block has a weight of 412N the other has a weight of 908N. we noticed that the hanging mass had a direct relationship with the angular acceleration. So if we add those accordingly with positives and negatives, we divide it by the total mass which gives the total measure of the inertia of our system. The rope and the pulleys are massless and there is no friction. and g, if there's no friction between m. c)Find the magnitude of the angular acceleration of the pulley. U = potential energy = volume = speed. Find the acceleration a and tension T in terms of m. with the same magnitude of acceleration. Learning objectives (students should learn…) – The significance and use of Newton’s second law of motion – To interpret physical meaning from graphs Equipment list:. At constant speed (no acceleration) the tension in the cord is the weight of block B = 2. 0 kg mass is attached to a 10. the acceleration system is. Once block. (a) What is the magnitude of the block's acceleration? (b) The force magnitude F is slowly increased. Purpose The purpose of this experiment is to demonstrate how imperfections in the experimental apparatus can play a large role in the final results. Physics 1120: Rotational Dynamics Solutions Pulleys 1. Note that the tension and acceleration of the two systems are exactly the same, because they are connected through the same lightweight string and the pulley is friction-less and has a neglected mass. friction! we already considered one contact force present when two surfaces touch, namely the normal force, which acts perpendicular to the surfaces! in some cases there can be a contact force parallel to the surfaces known as the friction force! friction is everywhere let’s build a simple model to describe it. Find acceleration aA of the pulley A in the gravity ﬁeld g As the rope is weightless, tension force T should be equal in any. time graph look like. 0 per- cent. The only force on it is , and it has the acceleration found above. tension should be constant, but less than “mg”. Transmitting power using shafts. µ = F / R = 10 / 50 = 0. Consider the situation shown at right, where the pulley is frictionless and massless. Dulku -Physics 20 -Unit 2 (Dynamics) -Topic I Newton's Laws and Pulley Systems Specific Outcome: i. Examples with Ropes and Pulleys We are still building our understanding of why do objects do what they do - in terms of forces. The pulley is assumed as mass less and friction free. (e) What is the mass of body 3?. The axle is connected to the support. The system is released from rest and there is no friction at all. Both m 1 and m 2 accelerate to the right at 3 m/s along the frictionless surface. Two masses, mA = 40. All the pulleys and strings are considered massless and there is no friction in the pulleys Note that top pulley doesn't move. Questions you may have include:. The problem asks in terms of m1, m2 and g (gravity), find the acceleration of each mass. A hanging mass will be attached to a glider placed. Determine the period that the spring mass system will oscillate for any non-zero initial conditions. The engine thrust just balances the air resistance and rolling friction (neither is given). have no friction, then the model reﬂects what we would expect. This video is useful for students. block and tackle) (3) the wheel and axle (4) the inclined plane (5. If pulley is light and frictionless then tension in the string on both sides is same. b) Find the magnitude of the tension of the string between m 1 and m2. I can further find Vmax knowing f s. However, the tension in both sections of rope is equal, even if both ends of the rope are being pulled by forces of different magnitudes. View our entire inventory of New or Used Snowmobiles. If there is no friction in this system, the net external force (Fnet) is the force of gravity (m2g) on the hanging mass m2; that is, Fnet = m2g. Calculations include conveyor capacity, belt speed, conveyor height and length, mass of idlers and idler spacing, belt tension, load due to belt, inclination angle of the conveyor, coefficient of friction, power at the drive pulley, starting belt tension, acceleration of the conveyor belt, and belt breaking strength, all with descriptions of. A formulated analysis of forces acting on a dynamics cart will be developed by the student. If you remember, there's a hard way to do this, and an easy way to do this. Find the acceleration and the tension in the rope of the system of masses shown (M > m), neglecting the mass of the string and the inertia of the pulley assume that the static and kinetic friction coefficients are equal to μ 1 μ 2 and the slope angle θ are known. Find the speed of 10 kg block as the 2kg leaves the ground. Solution: Concepts: Newton's second law, friction; Reasoning: There are two scenarios. B is set into downward motion, it descends at a constant speed. 010 m/s 2 , to assure an almost constant velocity motion. Pulley system on a double inclined plane. 0 degrees above the horizontal as shown. 1) F net,x ma x, F net,y ma y, F net,z ma z (5. In a physics lab, Kate and Rob use a hanging mass and pulley system to exert a 2. Formula: F = coefficent of friction*m*g 2)A 6. The system is released from rest. Imagine for example a car pulling two trailers. 1 Newton's First Law With Newton's Laws we begin the study of how motion occurs in the real world. The train (Figure 12) is moving with constant speed, so there is no tangential acceleration. b) Draw a free body diagram for m2. two blocks are connected by a rope that passes over a set of pulleys. 0 kg F a m = = = This is the acceleration of each piece of the system. Consider the situation shown at right, where the pulley is frictionless and massless. Note that this requires static friction operating between the string and the pulley. Newton's second law, F (force) = M (mass) x A (acceleration) assumes the pulley has no friction and you ignore the pulley's mass. The system in in a gravitational field of g, and the pulleys/strings are massless and there is no friction. 0 kg, are connected by a massless cord that passes over a pulley that is free to rotate about a fixed axis. To explore the effect of kinetic friction on motion. The string is generally connected to external objects. Cylinder B has a mass m is hoisted using the cord and pulley system shown. 250-kg object accelerating across a rough surface. But V-belt drive systems, also called friction drives (because power is transmitted as a result of the belt's adherence to the pulley) are an economical option for industrial, automotive. Newton's third law says that for every action there is an equal and opposite reaction, so the total force of the system F will equal the force in the rope or T (tension) + G (force of gravity) pulling at the load. If the total resistance force to the motion of the cart is 0. The tray and carton slide on a horizontal surface that is so greasy that friction can be neglected. The system is released from rest, and there is no friction at the axle of the pulley. To develop a clear concept of the idea of apparent weight. If the angle of the ramp is 28º and there is no friction, what is the acceleration of the blocks?. 8 A gear reduction system consists of three gears A, B, and C. attached by thin, very light wire wrapped around the rim of the drum (the figure ). The axle is connected to the support. As the tray moves, it pushes in turn on a 0. 0 kg block and a 3. The two block system shown above is dragged to the right at 5 m/s2. Therefore, to make things simple, we often use the massless and frictionless pulley approximation. A block of mass is sliding down the plane, as shown. Moment of inertia of pulley relative to the center of mass=2kgm2, M1=M2=0. (Newton = 1 kg x m/sec. And so on until infinity pulleys. A string connecting block 2 to a hanging mass M passes over a pulley attached to one end of the table, as shown above. 60 kg (use t= (2h/a)^(1/2) to find acceleration) A wooden block A of mass 4. Gear A starts from rest at time t = 0 and rotates clockwise with constant angular acceleration. a) Draw a free-body diagram for the load of bricks and a free-body diagram for the counterweight. 1 Newton's First Law With Newton's Laws we begin the study of how motion occurs in the real world. first of all, the total inertia of the system is going to include both blocks and the axle. P = power. The block 1 has a weight of 400 N, and the block 2 has a weight of 600 N. The purpose of this experiment is to explore the properties of kinetic friction. friction! we already considered one contact force present when two surfaces touch, namely the normal force, which acts perpendicular to the surfaces! in some cases there can be a contact force parallel to the surfaces known as the friction force! friction is everywhere let’s build a simple model to describe it. Find the acceleration a and tension T in terms of m. A string connecting block 2 to a hanging mass M passes over a pulley attached to one end of the table, as shown above. Physics problems: dynamics. Assuming no axle friction, determine the angular acceleration of the pulley and the acceleration of each block. The system is released from rest. first of all, the total inertia of the system is going to include both blocks and the axle. If the angle of the ramp is 28º and there is no friction, what is the acceleration of the blocks?. (Newton = 1 kg x m/sec. thanks in advance. Lever, pulley, wheel and axle, inclined plane, screw, wedge. again assuming that the system starts from rest in the position shown on the left above. 5 kg, are pulled to the right by a force P = 2. Now if the pulley is not frictionless (there is friction between the pulley and the cord), then the man must apply a greater force in order to support the box (because you are supporting the box and some of your force is dissipated due to friction) (the system here is also in equilibrium). a curve with an increasing slope Considering our pulley system with a mass falling at a constant acceleration, what should the general shape of its velocity vs. Neglecting friction, determine the acceleration of A, acceleration of B and tension in the cable after the system is released from rest. Friction always acts in the direction opposing motion. The system remains at rest this is what would happen if there were no. From the glider the string passed over a pulley mounted at the end of the track, and then downward to a weight hanger hooked to its lower end. If the actual acceleration with the fan generating the force calculated in part a is only 4. They are typically used for hauling and lifting loads but can also be used to apply tension within a system such as in a Tensioned Line or Tyrolean. 6F If frictionless, gravity does not affect horizontal motion 8. What will become of these two knights? Find out in Ideology in Friction!. Block on an Incline Adjacent to a Wall A wedge with an inclination of angle rests next to a wall. Newton's 2nd Law (12 of 21) Calculate Acceleration w/o Friction; Inclined Plane, Pulley, Two Masses Shows how to calculate the acceleration and tension in the string for a two block system on an inclined plane without friction using Newton' Second Law. There is a 0. a stretchless, massless cord that passes over a small frictionless pulley. Question 12 Find the acceleration of the block assuming no friction is present (a) F/2m (b) F/m (c) 2F/m (d) none of the above Question 13 If friction force F/4 exist between the block and surface (a) F/m (b) F/m (c) F/4m (d) none of the above Linked Comprehensive type (C). The coefficient of friction between the block and the table is \mu= The pulley is frictionless. If the blocks accelerate with a magnitude of a, then the pulley will experience an angular acceleration of alpha=a/R, since the acceleration of the outer-most part of the pulley is alpha*R. What is the acceleration of the 2. We changed the hanging mass in experiments 1,2 and 3. The maximum static friction is usually greater than the kinetic friction between the. (Figure 1) Block 1, of mass m1 = 0. When this system is released from rest, the pulley turns through 0. If the blocks accelerate with a magnitude of a, then the pulley will experience an angular acceleration of alpha=a/R, since the acceleration of the outer-most part of the pulley is alpha*R. The first is the normal force N is always perpendicular to the surface. The system is released from rest, and there is no friction at the axle of the pulley. There are two types of friction – static and kinetic. A fixed (attached to a non-moving object) pulley changes the direction but not magnitude. two blocks are connected by a rope that passes over a set of pulleys. Applying force F to the mass in a pulley system will be much lesser than if compared to the force we need to exert if without the pulley. As part a of the drawing shows, two blocks are connected by a rope that passes over a set of pulleys. Two objects of mass 6 kg and 4 kg are connected to a string that goes over a smooth pulley. 4? We will start our solution by examining freebody diagrams and the static equilibrium equations: Σ F x = 0 and Σ F y = 0. The block is connected to a cord of negligible mass, which. 74 m s 2 23. A rope is attached and positioned over a pulley at the top of the incline. an example is here in the image of what im trying to build , now the speed is unrelevent aslong as its rotating even if its very slow. Other pulley designs will call for various strengths of lines and pulleys based on their status in the system. a) the angular acceleration of the pulley and. The block on the table has mass m 1 = kg and the hanging block has mass m 2 = kg. The systems basically include different groups of pulley/string mechanisms, each involving a specific pattern of movement for lifting the attached weight in response to the applied effort. Calculate the acceleration of the system in Figure 2. Last Revised on January 8, 2015 Grade: _____ Experiment 2 Acceleration of Gravity 1. Once block. 91 N and block B has weight 2. I have a mass on a low friction track with a string connected over a pulley to a hanging mass. Pulley with mass and two blocks - Mechanics Question 349. The rope and the pulleys are massless and there is no friction. Examining the problem object by object we see that the spring stretches, so there is an increase in spring potential energy. Friction allows us to move, which you have discovered if you have ever tried to walk on ice. 2016 (a) OL Masses of 1 kg and 4 kg are connected by a taut, light, inextensible string which passes over a smooth light fixed pulley. We’re stating our assumptions (that the rope is massless and the pulley is frictionless), restating our known variables (the kinetic coefficient of friction, the two masses of the blocks, the acceleration of the system), and identifying the two unknowns that we need to find (the tension in each section of rope). Mechanical energy is not conserved. Friction and Motion on Inclined Planes Written by tutor Alex F. (a) Using conservation of energy (assuming no friction between cart and axles), and assuming pure rolling motion (no slipping), show that the acceleration of the cart along the incline is (b) Note that the x component of acceleration of the ball released by the cart is g sin. 0 kg block and a 3. It will also be equal to Mg-Ma for the large mass object falling. Problem 1 (No friction) A 2 Kg box is put on the surface of an inclined plane at 27 ° with the horizontal. Consider the system shown in the figure (shown below). Mass in the SI system is measured in kilograms (kg). force, we were able to calculate the coefficient of kinetic friction for that trial using equation 8. a) Force diagrams: 3. hi, im stuck in a part of a project, im not the strongest in physics and here im trying to build a system but im struggling to calculate the torque needed to rotate a load via belt attached to a pulley and that pulley attched to a motor. L = angular momentum = length. Fill in the spring-scale readings that show how much force she must exert. friction between the disks is Pk = 0. Can you figure out the acceleration of the cart -- which is the same as that of the weight -- in the presence of friction?. Assume that the pulley rotates without friction and there is no slipping of the string. Formula: F = coefficent of friction*m*g 2)A 6. is released from rest, it experiences a constant (and non-zero) acceleration. 0 m/s2, what is the force of friction on the crate? (c) What is the maximum acceleration the truck can have without the crate starting to slide? (a) Since the truck is not accelerating, there is no external force on the crate in the. The system is released from rest, and there is no friction at the axle of the pulley. • To practice the use free-body diagrams (FBDs). Assuming that M > m, find the acceleration of the ribbon along the prism after the blocks are simultaneously released. 0 kg mass hangs off the edge of the table. Ok, so on to our first project displayed in this blog. 5 m and lands. I can further find Vmax knowing f s. Man A climbs up the rope with acceleration a relative to the rope. Recitation Week 4 Chapter 5 Problem 5. There are two bodies in the system, and we draw free-body diagrams of each of them. Gear A starts from rest at time t = 0 and rotates clockwise with constant angular acceleration. • b) Determine the acceleration of the two blocks. This physics video tutorial explains how to calculate the acceleration of a pulley system with two masses with and without kinetic friction. Find the magnitude of the acceleration with which the bucket and the block are moving and the magnitude of the tension force T by which the rope is stressed. friction between the disks is Pk = 0. The truck starts moving up a 20°slope. (m 1 + m 2)g c. Find the acceleration experienced by each of the two objects shown in the gure if the coe cient of kinetic friction between the 7. Without friction, the acceleration in the system is shown by the equation: Step 2. You can't. massless string from a pulley. b) Find the tension in each part of the string. In this problem, you are asked to relate motion (the acceleration of the two blocks) to force (tension in the rope, friction). Block on an Incline Adjacent to a Wall A wedge with an inclination of angle rests next to a wall. 20, calculate the acceleration of each body and the tension T in the cable. Just as friction accounted for the deviation from the ideal acceleration in the previous approach, it should also account for any changes in the energy in the latter approach. Formula: F = coefficent of friction*m*g 2)A 6. Once the total added mass reached 250 g, we found an average of the coefficient of friction values, as shown below:. Calculate the acceleration of the system. The sliding object is attached by a string to a 0. The tension forces in the ropes are T1, T2, and T3, and the mass of the hanging ball is m= 3. The block on the table has mass m 1 = kg and the hanging block has mass m 2 = kg. According to Newton’s 2nd Law, the acceleration of a system is _____ proportional to the total mass of the system and _____ proportional to the net force acting on the system. 5kg, R2=2R1=0. At the instant after the system of objects is released, find (a) the tension T in the string, (b) the acceleration of m2, (c) the acceleration of M, and (d) the acceleration of m1. The cord has a negligible mass and causes the pulley to rotate without slipping. Note that this requires static friction operating between the string and the pulley. 91 N and block B has weight 2. the body's mass and its acceleration. Pulleys are useful for us to lift objects as they reduce the amount of force we need to exert. (Newton = 1 kg x m/sec. the pulley is pulled up with a force F = 50 N. What time does it take a box with mass m 1 to go down a distance s on an inclined plane with a slope of angle α when the box is coupled by a rope and a pulley to a bucket with mass m 2? The proportion m 1 /m 2 is such that the box moves down the inclined plane. (Assume the same μk for both blocks in contact with surfaces. The only force on it is , and it has the acceleration found above. 7 kg) is initially moving to the left. Physics 204A Problem Set #13 1. Neglect the small mass and friction of the pulleys. The friction force depends on the mass of an object plus the coefficient of sliding friction between the object and the surface on which it slides. What is the normal force (N) on M ?. The cœfficient of kinetic friction Ml and the table is les than the coefficient of static friction k. 010 m / s 2 to assure an almost constant velocity motion. a) Force diagrams: 3. 09kg and the smaller bloc. 74 m s 2 23. ) • c) Determine the tensions in the string on both sides of the pulley. A fixed (attached to a non-moving object) pulley changes the direction but not magnitude. Draw a diagram of the pulley system described in this problem. 5 N, acts on it directed at an angle of 35. Exactly like the basic pulleys, the ropes on either side of the moving pulley contribute. What factors affect the motion of an. The block is connected to a cord of negligible mass, which. The angular position of a point on a wheel is described by. In this applet, a zero acceleration means no motion; therefore, try to keep the acceleration nearly zero, under 0. Suppose friction is present. If pulley is light and frictionless then tension in the string on both sides is same. = acceleration. If the angle of the ramp is 31 degrees and the coefficient of kinetic friction is 0. Here is a representative inclined plane problem which ignores the effects of friction. None of these choices. by Ron Kurtus (revised 21 October 2016) The standard friction equation shows the relationship between the resistive force of friction, the coefficient of friction and the normal force pushing the objects together. friction! we already considered one contact force present when two surfaces touch, namely the normal force, which acts perpendicular to the surfaces! in some cases there can be a contact force parallel to the surfaces known as the friction force! friction is everywhere let's build a simple model to describe it. In the system in the diagram below, block M (15. in grams (g) and centimeters (cm) so you will be using the cgs system of units instead. Newton’s second law for mass M is. A = amplitude. In the past, we assumed that the cart rolled and the pulley rotated without friction. In this applet, a zero acceleration means no motion; therefore, try to keep the acceleration nearly zero, under 0. Determine the acceleration of the system. Treat the pulley as a uniform disk. The force of friction will oppose the downhill component of the gravitational force. ( spring constant,k= 40 N/m and take g = 10 m/s² ). Solving this system of equations, the expressions for the tension and the acceleration are: $$ T = \frac{2m_{1}m_{2}}{m_{1}+m_{2}}g \tag{3} $$. Pulley – 1. Dynamics - Freefall, Apparent Weight, and Friction (Honors) PURPOSE To investigate the vector nature of forces. the acceleration system is. We started with no mass on the wooden block, then we added a 50 g mass to the block for each successive trial. Q4) A pulley is made from a solid disk of radius 15 cm and mass 400 grams, and rotates with no friction. Simplify and Diagram Assume that the pulley’s mass is very small and rotates without friction. Materials/Equipment (per team) Computer with Logger Pro software installed – 1. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: