Advertisements
Advertisements
Question
Figure shows the position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the body ? What is the magnitude of each impulse ?
Advertisements
Solution 1
A ball rebounding between two walls located between at x = 0 and x = 2 cm; after every 2 s, the ball receives an impulse of magnitude 0.08 × 10–2 kg m/s from the walls
The given graph shows that a body changes its direction of motion after every 2 s. Physically, this situation can be visualized as a ball rebounding to and fro between two stationary walls situated between positions x = 0 and x = 2 cm. Since the slope of the x-t graph reverses after every 2 s, the ball collides with a wall after every 2 s.
Therefore, ball receives an impulse after every 2 s.
Mass of the ball, m = 0.04 kg
The slope of the graph gives the velocity of the ball. Using the graph, we can calculate initial velocity (u) as:
`u = ((2-0)xx10^2)/(2-0) = 10^(-2) "m/s"`
Velocity of the ball before collision, u = 10–2 m/s
Velocity of the ball after collision, v = –10–2 m/s
(Here, the negative sign arises as the ball reverses its direction of motion.)
Magnitude of impulse = Change in momentum
=|mv - mu|
=|0.04 (v -u)|
=|`0.04(-10^(-2)- 10^(-2))`|
= 0.08 × 10–2 kg m/s
Solution 2
This graph can be of a ball rebounding between two walls situated at position 0 cm and 2 cm. The ball is rebounding from one wall to another, time and again every 2 s with uniform velocity.
Impulse, Here velocity = `("displacement")/"time" = 2/(100xx2) = 0.01 ms^(-2)`
Initial momentum = mu = `0.04 xx 0.01 = 4 xx 10^(-4) "kg ms"^(-1)`
Final momentum = mv = `0.04 x (-0.01) = -4 xx 10^(-4) "kg ms"^(-1)`
Magnitude of impulse = Change in momentum
=`(4xx 10^(-4)) -(-4xx10^(-4)) = 8 xx 10^(-4) kg ms^(-1)`
Time between two consecutive impulses is 2 s.i.e the ball receive an impulse every 2 s
RELATED QUESTIONS
An object of mass 1 kg travelling in a straight line with a velocity of 10 ms−1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.
Name the physical quantity which is considered to be a measure of the quantity of motion of a body.
What is the change in momentum of a car weighing 1500 kg when its speed increases from 36 km/h to 72 km/h uniformly ?
What is the momentum in kg.m/s of a 10 kg car travelling at (a) 5 m/s (b) 20 cm/s, and (c) 36 km/h ?
Define momentum of a body. On what factors does the momentum of a body depend ?
State the relation between the momentum of a body and the force acting on it.
Which physical principle is involved in the working of a jet aeroplane ?
Fill in the following blanks with suitable words :
Momentum is a _____________ quantity. Its unit is _____________.
A 10 g bullet travelling at 200 m/s strikes and remains embedded in a 2 kg target which is originally at rest but free to move. At what speed does the target move off ?
A body of mass 2 kg is at rest. What should be the magnitude of force which will make the body move with a speed of 30 m/s at the end of 1 s ?
Why would an aircraft be unable to fly on the moon ?
Explain why it is possible for a small animal to fall from a considerable height without any injury being caused when it reaches the ground.
A boy of mass 50 kg running at 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s. What is their common velocity ?
A man wearing a bullet-proof vest stands still on roller skates. The total mass is 80 kg. A bullet of mass 20 grams is fired at 400 m/s. It is stopped by the vest and falls to the ground. What is then the velocity of the man?
Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of the initial and final momentums of the ball are the same. Yet, it is not an example of conservation of momentum. Explain why?
Two billiard balls A and B, each of mass 50 g and moving in opposite directions with speed of 5 ms–1 each, collide and rebound with the same speed. If the collision lasts for 10–3 s, which of the following statements are true?
- The impulse imparted to each ball is 0.25 kg ms–1 and the force on each ball is 250 N.
- The impulse imparted to each ball is 0.25 kg ms–1 and the force exerted on each ball is 25 × 10–5 N.
- The impulse imparted to each ball is 0.5 Ns.
- The impulse and the force on each ball are equal in magnitude and opposite in direction.
A girl riding a bicycle along a straight road with a speed of 5 ms–1 throws a stone of mass 0.5 kg which has a speed of 15 ms–1 with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?
A monkey of mass 20 kg rides on a 40 kg trolley moving with constant speed of 8 m/s along a horizontal track If the monkey jumps vertically to grab the overhanging branch of a tree, the speed of the trolley after the monkey has jumped off is ______.
