Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given, the total mass of girl, bicycle and stone = m1 = (50 + 0.5) kg = 50.5 kg.
Velocity of bicycle u1 = 5 m/s, Mass of stone m2 = 0.5 kg
Velocity of stone u2 = 15 m/s, Mass of girl and bicycle m = 50 kg
Yes, the speed of the bicycle changes after the stone is thrown.
Let after throwing the stone the speed of bicycle is v ms.
According to the law of conservation of linear momentum,
m1u1 = m2u2 + mv
50.5 × 5 = 0.5 × 15 + 50 × v
252.5 – 7.5 = 50 v
or v = `245.0/50`
v = 4.9/m/s
Change in speed = 5 – 4.9 = 0.1 m/s.
APPEARS IN
RELATED QUESTIONS
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s−1. Calculate the initial recoil velocity of the rifle.
Name the physical quantity which is considered to be a measure of the quantity of motion of a body.
Name the physical quantity whose unit is kg.m/s.
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 ?
A man throws a ball weighing 500 g vertically upwards with a speed of 10 m/s.
- What will be its initial momentum ?
- What would be its momentum at the highest point of its flight ?
Name the principle on which a rocket works.
A gun of mass 3 kg fires a bullet of mass 30 g. The bullet takes 0.003 s to move through the barrel of the gun and acquires a velocity of 100 m/s. Calculate:
- the velocity with which the gin recoils.
- the force exerted on gunman due to recoil of the gun
Name the law involved in the following situation :
the sum of products of masses and velocities of two moving bodies before and after their collision remains the same.
Explain why, a cricket player moves his hands backwards while catching a fast cricket ball.
A 150 g ball, travelling at 30 m/s, strikes the palm of a player’s hand and is stopped in 0.05 second. Find the force exerted by the ball on the hand.
State the law of conservation of momentum.
Discuss the conservation of momentum in each of the following cases :
(i) a rocket taking off from ground.
(ii) flying of a jet aeroplane.
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 girl of mass 50 kg jumps out of a rowing boat of mass 300 kg on to the bank, with a horizontal velocity of 3 m/s. With what velocity does the boat begin to move backwards ?
A truck of mass 500 kg moving at 4 m/s collides with another truck of mass 1500 kg moving in the same direction at 2 m/s. What is their common velocity just after the collision if they move off together ?
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?
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 ______.
Two blocks P and Q of masses 0.3 kg and 0.4 kg, respectively, are stuck to each other by some weak glue as shown in the figure. They hang together at the end of a spring with a spring constant of k = 200 N/m. The block Q suddenly falls free due to the failure of glue, then the maximum kinetic energy of block P during subsequent motion will be ______ mJ.
