Question

This question is a long free-response question. Show your work for each part of the question.

The figure presents a diagram of three blocks, labeled 1 through 3. In the diagram, block 1 is resting on the floor. Block 2, which is smaller than block 1, is resting on top of block 1. Block 3, which is approximately the same size as block 1, is resting on a table. The right side of block 3 is attached to one end of a string which runs over a pulley located at the right edge of the table. The other end of the string is attached to the top of block 2.

Block 1 is resting on the floor with block 2 at rest on top of it. Block 3, at rest on a smooth table with negligible friction, is attached to block 2 by a string that passes over a pulley, as shown above. The string and pulley have negligible mass.


(a)


i. On the dot that represents block 1, draw and label the forces (not components) exerted on block 1. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. Draw the relative lengths of all arrows to reflect the relative magnitudes of the forces.


The figure presents a 6 by 6 grid with a dot in the center, labeled "Block 1. "



Question 2

ii. On the dot that represents block 2, draw and label the forces (not components) exerted on block 2. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. Draw the relative lengths of all arrows to reflect the relative magnitudes of the forces.


The figure presents a 6 by 6 grid with a dot in the center, labeled "Block 2. "


Question 3

(b) Block 1 is removed without disturbing block 2.


i. Consider the scenario where the mass m3 of block 3 is greater than the mass m2 of block 2. Without using equations, make a claim about the motion of block 3 in terms of balanced or unbalanced forces.


Block 3 will move to the right because friction is negligible so Fg would move block 2 down and therefore, tension would pull block 3.


Question 4

ii. Derive an equation for the acceleration of block 3 for any arbitrary values of m3 and m2. Express your answer in terms of m3, m2, and physical constants as appropriate.



Question 5

(c) Describe in what way your answer to part (b)(ii) is or is not consistent with your claim in part (b)(i).


It is consistent with bi because the block3 will be moving to the right.


Question 6

(d) On the axes below, sketch graphs of the velocity and the acceleration of block 2 after block 1 has been removed. Take the time to be zero immediately after block 1 has been removed

Answer 1

(a)

i. On the dot that represents block 1, the forces exerted on block 1 are:

- The gravitational force (mg), which points downward.

- The normal force (N) exerted by the floor, which points upward.

ii. On the dot that represents block 2, the forces exerted on block 2 are:

- The gravitational force (mg), which points downward.

- The normal force (N) exerted by block 1, which points upward.

- The tension force (T) exerted by the string, which points upward.

(b)

i. When block 1 is removed without disturbing block 2, block 3 will move to the right. This is because the mass of block 3 (m3) is greater than the mass of block 2 (m2), and the tension force in the string will pull block 3 to the right.

ii. To derive an equation for the acceleration of block 3, we can consider the forces acting on it. The net force on block 3 is the difference between the tension force (T) and the gravitational force (m3g):

Net force = T - m3g

Using Newton's second law (F = ma), we can relate the net force to the acceleration:

T - m3g = m3a

Therefore, the equation for the acceleration of block 3 is:

a = (T - m3g) / m3

(c)

The answer to part (b)(ii) is consistent with the claim made in part (b)(i). Both state that block 3 will move to the right. In part (b)(ii), we derived an equation for the acceleration of block 3, which shows that the acceleration depends on the tension force (T) and the difference between the masses of block 3 and block 2. The equation confirms that block 3 will accelerate to the right.

(d)

To sketch the graphs of the velocity and acceleration of block 2 after block 1 has been removed, we need more information such as the relationship between the masses of block 1, block 2, and block 3, as well as the nature of the pulley system. Without this information, it is not possible to accurately sketch the graphs.