A large block is resting on the table. On top of that block...

A large block is resting on the table. On top of that block rests another, smaller block, as shown in Fig. 6-88. You press on the larger block to start it moving. After about $0.25$ s, it is moving at a constant speed and the block on the top is not slipping. (a) Draw a labeled free-body diagram for the two blocks $d u r$ ing the time when they are accel. erating, specifying all the forces acting on the blocks. (Be sure to specify the type of force and the object causing each force.) Wherever you can, compare the magnitudes of forces. (b) Draw a labeled free-body diagram for the two blocks during the time when they are moving at a constant speed, specifying all the forces acting on the blocks. (Be sure to specify the type of force and the object causing each force.) Wherever you can, compare the magnitudes of forces. (c) Suppose the bottom block has a mass of $0.4 \mathrm{~kg}$ and the coefficient of friction between the block and the table is $0.3$. The top block has a mass of $0.1 \mathrm{~kg}$ and the coefficient of friction between the two blocks is $0.2$. What force do you need to exert to keep the blocks moving at a constant speed of $10 \mathrm{~cm} / \mathrm{s} ?$ (You may use $g=$ $10 \mathrm{~N} / \mathrm{kg}$ and you may treat kinetic and static friction as the same.)

A large block is resting on the table. On top of that block rests another, smaller block, as shown in Fig. 6-88. You press on the larger block to start it moving. After about $0.25$ s, it is moving at a constant speed and the block on the top is not slipping.
(a) Draw a labeled free-body diagram for the two blocks $d u r$ ing the time when they are accel. erating, specifying all the forces acting on the blocks. (Be sure to specify the type of force and the object causing each force.) Wherever you can, compare the magnitudes of forces.
(b) Draw a labeled free-body diagram for the two blocks during the time when they are moving at a constant speed, specifying all the forces acting on the blocks. (Be sure to specify the type of force and the object causing each force.) Wherever you can, compare the magnitudes of forces.
(c) Suppose the bottom block has a mass of $0.4 \mathrm{~kg}$ and the coefficient of friction between the block and the table is $0.3$. The top block has a mass of $0.1 \mathrm{~kg}$ and the coefficient of friction between the two blocks is $0.2$. What force do you need to exert to keep the blocks moving at a constant speed of $10 \mathrm{~cm} / \mathrm{s} ?$ (You may use $g=$ $10 \mathrm{~N} / \mathrm{kg}$ and you may treat kinetic and static friction as the same.)

Key Concepts

Free-Body Diagram

A free-body diagram is a graphical illustration used to depict all the forces acting on an object. It plays a fundamental role in physics problems by allowing one to account for gravitational, normal, frictional, and applied forces, helping to set up the equations of motion for analysis.

Newton's Laws of Motion

Newton's laws, especially the second law, are central to understanding the motion of objects. The second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration, which is critical whether the system is accelerating or moving at constant speed.

Frictional Forces

Friction is the resistive force that acts opposite to the direction of relative motion between surfaces. It can be either static, preventing motion until a threshold is overcome, or kinetic, opposing motion when objects slide against each other. In problems where slipping is prevented, the appropriate frictional force must be considered to maintain the non-slip condition.

Constant Velocity vs. Acceleration

When an object moves at constant velocity, its acceleration is zero, indicating that all the forces are balanced. In contrast, when an object accelerates, there is an imbalance of forces. Analyzing both situations requires careful consideration of net forces acting on the system during acceleration and during steady motion.

Non-Slip (No Relative Motion) Condition

The non-slip condition ensures that two contacting bodies move together without sliding relative to one another. This requires that the frictional force between the bodies is sufficient to overcome any tendency to slip, ensuring that both bodies share the same acceleration during motion.

Transcript

00:01 In this question we have given that of two blocks that is placed at one another and we need to find that we need to find the different scenarios from the given okay so now we have given two blocks right so basically one each one is bigger so let me draw it so this is the first block this is the second block right this is block b and a p and a okay this is we are pulling with the force support over there okay so in the first scenario draw the and we have given that the top of the block and you you place the longer block to the start it's moving after about 0 .25 seconds it is moving in a constant speed and the block on the top is not so draw all level three body diagram for the two blocks during the time when they are accelerating space high all the forces so basically so the free body diagram for this two will be nothing but in the first part.

01:11 For the block a, there will be mg force and over here one more force because b is also at the a.

01:17 So that means the mg, mg, mg, m2, mbg will be as well because they are also placing the same thing.

01:25 And normal will be these two due to there is no motion in this one.

01:28 So not only this one plus this one.

01:30 Now, if there is a frictional force, so that will, if the block is moving in this direction, so there will be a friction force due to a on v and in this direction right and for the block b there will be m m v g downward at the block a and obviously there will be force over here also due to the block b that means mvg and normal as well so over here mbg and normal as well and now there will be of course due to since there is friction force is due in this direction so friction force due to this in this direction right and this will be the diagram and when they are moving with the constant velocity so in the second scenario draw the level body diagram to block during the time when they are moving in the constant space when they are constant speed that means that means the acceleration is zero that means there is no net force so that means and obviously there will be friction as well over here there will be f over here and f over here in this direction and friction force in this direction as well and in this scenario, if this is a and this is b, so f over here that will fix and force that will be equal and this will be total m1ma plus mb, g, and over here that will be total normal because they are in the constant, you know, zero acceleration, okay? and obviously there will be some contact force over here as well that will fix an in this reaction and normalization and this will be balanced out because there is no acceleration...

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