Newton’s Second Law corrected the old belief that force is needed to maintain motion. This idea came from the philosopher ______.
Advertisements
Advertisements
Question
A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end in the following figure. Show that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.
Numerical
Advertisements
Solution
Suppose the monkey accelerates upward with acceleration a and the block accelerates downward with acceleration a1.
Let force exerted by the monkey be F.
From the free-body diagram of the monkey, we get:
F− mg − ma = 0 ...(i)
⇒ F = mg + ma
Again, from the free-body diagram of the block,
F + ma1 − mg = 0
mg + ma + ma1 − mg = 0 [From (i)]
⇒ ma = −ma1
⇒ a = −a1
If acceleration −a1 is in downward direction then the acceleration a1 will be in upward direction.
This implies that the block and the monkey move in the same direction with equal acceleration.
If initially they were at rest (no force is exerted by the monkey), then their separation will not change as time passes because both are moving same direction with equal acceleration.
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]
| Lowest Point | Highest Point | |
| a) | mg – T1 | mg + T2 |
| b) | mg + T1 | mg – T2 |
| c) | `mg + T1 –(m_v_1^2)/R` | mg – T2 + (`mv_1^2`)/R |
| d) | `mg – T1 – (mv)/R` | mg + T2 + (mv_1^2)/R |
T1 and v1 denote the tension and speed at the lowest point. T2 and v2 denote corresponding values at the highest point.
A small block B is placed on another block A of mass 5 kg and length 20 cm. Initially, the block B is near the right end of block A (In the following Figure). A constant horizontal force of 10 N is applied to the block A. All the surfaces are assumed frictionless. Find the time that elapses before block B separates from A.
The monkey B, shown in the following figure, is holding on to the tail of monkey A that is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg, respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry monkey B with it? Take g = 10 m/s2.
Define linear momentum and state its S.I. unit.
Two balls A and B of masses m and 2 m are in motion with velocities 2v and v, respectively. Compare:
(i) Their inertia.
(ii) Their momentum.
(iii) The force needed to stop them in the same time.
Calculate the magnitude of force which when applied on a body of mass 0.5 kg produces an acceleration of 5 m s-2.
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : The velocity acquired by the body
A bullet of mass 50 g moving with an initial velocity 100 m s-1 strikes a wooden block and comes to rest after penetrating a distance 2 cm in it. Calculate: (i) Initial momentum of the bullet, (ii) Final momentum of the bullet, (iii) Retardation caused by the wooden block and (iv) Resistive force exerted by the wooden block.
A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g = 10 m s-2 and speed of sound = 330 m s-1. Find : The time when echo is heard after the pebble is dropped.
What do you understand by the term momentum?
State two factors which determine the momentum of a body.
Multiple Choice Question. Select the correct option.
A force acts on a body of mass 3 kg such that its velocity changes from 4 ms−1 to 10 ms−1. The change in momentum of the body is
Name the physical entity used for quantifying the motion of a body.
Which of the following has the largest inertia?
Use Newton's second law to explain the following:
We always prefer to land on sand instead of hard floor while taking a high jump.
A stone is dropped from a cliff 98 m high.
What will be its speed when it strikes the ground?
The INCORRECT statement about Newton's second law of motion is
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
What happens when a car brakes to come to a stop?
