(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.