Is momentum conserved, is used chiefly while considering collisions between objects in contact.
Momentum distinguishes that locomotion does not change in a closed system of bodies. Conservation word means to something that does not change and maintain its state.
How is momentum conserved?
The momentum, the product of mass and velocity, gets conserved.
To understand how the momentum gets conserved, let us take the example of two objects. Two objects, namely object A and object B, when they both collide in a closed system. The total momentum means the momentum of object A and object B gets conserved. The total momentum of the two objects is conserved.
This means that when the object strikes, object A and object B’s shared momentum is identical to the total momentum of object A and object B after the impact. Therefore, the momentum of object A lost is identical to the momentum acquired by object B.
We can say that the momentum remains the same for the objects or gets conserved. Here as the momentum of object A and object B remains conserved or, say, maintain their state, this is in accordance with the law of conservation of momentum.
When is momentum conserved?
As said above, conservation of momentum is considered while discussing any collision, explosions, the motion of objects, etc.
So the momentum of objects gets conserved when they are involved in any motion, or say collision. Conserving their momentum means that they do not change their state and remain constant throughout the action. And if this happens, then it is said that the total momentum is conserved for the body.
Is momentum conserved in all collisions?
According to the law of conservation, momentum gets conserved until no external force acts upon the system in motion.
And when to bodies collide, or say when they are in collision. No external force acts upon them during their collision. Therefore, we can say that the total momentum gets conserved in collisions by following the law of conservation. However, the energy involved in the collision gets changed in the collision, whereas kinetic energy gets altered due to the dissipation of energy in some other form.
Is momentum conserved in free fall?
Earth has its gravitational pull, and it acts upon the body falling with the same pull as the free-falling body.
During a free fall by any object from a height on earth. The body gains some momentum as it has some mass and is in motion, having some velocity. The earth counters the downward momentum created by the object in a free fall.
Because of this gravitational force, the free-falling body and earth are taken to a fastened system where no external force acts upon it. Hence the free-falling body and earth are in an isolated system. Due to this influence of the earth’s gravitational pull, the total momentum of the free-falling body is conserved. As the momentum by the free-falling body and they remain same.
Is momentum conserved when a ball hits a wall?
We know that when a ball hits a wall, it is not considered a closed system. And the law of conservation of momentum is applied in a closed system, which means that no external force acts upon the objects into collision.
When the ball hits the wall, in this condition, the wall brings to bear an opposite force to the ball. This can be understood why this happens by Newton’s third law of motion. So as the ball exerts an external force that is a force from the wall, the law of consecration of momentum is not applied.
Hence, the momentum of the ball gets changed while hitting.
Problems related to momentum
Q. A friction-less surface has an embedded bullet in it because of firing by a bullet. Explain what gets conserved in this process.
The bullet is embedded in the surface in the given situation, where no external force is applied. We can say that the momentum gets conserved in the process. However, as it is an inelastic collision, kinetic energy is not conserved.
Q. A train is moving with a velocity of 100m/s. If the train’s momentum is found to be 10000 kg m/s, then find what will be its mass?
Given, Momentum (p) = 10000 kg m/s
Velocity (v) = 100m/s
Mass (m) =?
By momentum formula we know that:- Momentum (p) = Mass (m)*Velocity (v)
so by putting value of each we get,
m =100 kg
Thus, we know that the mass of the train is 100 kg.
Q. A truck of mass 400 kg is moving at 20 m/s. Now find its initial momentum. When The driver accelerated the truck, a force of 100 N acted upon the truck for 8 seconds. Now find the final momentum.
By the formula, we know that,
Initial momentum= mass*initial velocity = 400*20 kg m/s = 8000 kg m/s
so, the Impulse of the force = force*times time taken = 100* 8 N = 800 N
and We already know that the, impulse of force = change of momentum
As given in the question, the truck accelerate
final momentum = initial momentum + impulse of force = (8000 + 800) kg m/s =8800 kg m/s
Q. Explain whether the law of conservation of momentum is violated or not in the process. When thrown in an upward direction, a ball, during its throw, the ball momentum is first decreased, and then it starts increasing.
In the earlier scenario, the ball’s momentum and earth remain conserved. When the ball is launched upward, an attractive force is brought into play.
This force is equal from both sides, the earth, and the ball, respectively. However, When the ball goes upward, its momentum starts to decline while going up, but during the same duration, the earth’s momentum also increases at the same rate in the upward direction. And accordingly, when the ball starts its downward fall, its momentum tends to increase in the downward direction. In the course, the earth’s momentum also escalates simultaneously in the upward direction.
Q. Examine the given situation. A rope is hanging from a tree and fastened from one end. On the rope, grapes are tied on the upper-end side. At the same time, the monkey is hanging on the lower end of the rope fastened to the tree. Here The mass of the monkey is equal to the mass of the grapes tied to the rope. Now explain whether the monkey would eat the grapes if it starts to climb up the rope.
In the given situation, the monkey will not be able to eat grapes. as when the monkey starts to climb up the rope, the grape tied to the rope will also move upward equally so that the momentum remains conserved.
In these circumstances, the momentum gets overturned due to the branch of the tree on which the rope is fastened as it acts as a sheave. This happened so that their combined momentum persisted in being 0.
Q. There are Two boys having the same mass. Both of them are standing on ice skates at some distance apart from each other on a friction-less surface. A rope is tied around the waist of a boy, the other end of the rope is in the hand of the second boy. What would happen if the second boy pulled the rope?
When the boy holding the other end of the rope draws the other boy towards him then, both the boys will start to proceed toward each other. The speed with which they will move will be the same. This phenomenon occurs so that their momentum remains zero or maintains the state.
Q. When the air is blown on a sail attached to a boat through an electric fan placed on the boat. Tell me whether the boat will start moving or not?
No, the boat will not move through the following actions. While blowing the air to sail through the air by a fan, the air itself pushes back the fan in contradistinction. Here the sum of fan and boat momenta will be 0. The boat will move but under the reaction force from some external agent.