Momentum = mass × velocity
Example
- A body of mass 6kg moves with a velocity 20m/s. calculate the momentum of the body
Solution
Momentum = mass × velocity
= 6 × 20 = 120kgm/s
Impulse can be defined as the product of the force and the time it takes to acts on a body. For example a tennis player with a bat in his hand, the moment the ball comes to his spot, the product of the force he applies to the ball and the time it take the bat to make contact with the ball is called Impulse. Impulse is a vector quantity and its unit is Ns.
Impulse = force × time
Example
- A stationary ball is hit by an average force 100N for a time of 0.02sec. What is the impulse experienced by the body?
Impulse = force × time
= 100 × 0.02 = 2Ns
- A ball of mass 20kg strikes a vertical wall and rebounce with the same velocity. If the Impulse received is 1.2KNs. The magnitude of the velocity is ______
The tendency of a body to remain in its state of rest or uniform motion in a straight line is called inertia. Newton’s first law of motion is also called the law of inertia.
This law states that the rate of change of momentum is directly proportional to the force and it takes place in the direction of that force. When we say change in momentum, It means there is initial momentum ( mu) and final momentum (mv). Mathematically, it can be express as
Note: When you are given a question and it has to do with rebound, we use this simple formula
Change in momentum = mv + mu
Let's take a question to understand this
- A body of mass 100g moving with a velocity of 10m/s collides with a wall. If after the collision, it moves with a velocity of 2m/s in the opposite direction. calculate the change in momentum
Solution
Question
- A constant force of 5N acts for 5sec on a mass of 5kg initially at rest. Calculate the final momentum
- A ball of mass 0.3kg, moving at a velocity of 10m/s is suddenly hit by a force of 3N for a time of 0.02sec. Find its new velocity of motion.
Solution
- A 20g bullet moving at 200m/s hits a bag of sand and comes to rest in 0.011s.
(a) What is the momentum of the bullet just before hitting the bag
(b) Find the average force that stop the bullet
The fuel in the engine of a Jet/rocket undergoes combustion which releases a gas that propels the jet to move forward thereby obeying Newton’s third law of motion.
This principle state that if two bodies collide in a closed system, the total momentum before collision is equal to the total momentum after collision. The following steps can be use to understand this principle.
MAUA + MBUB = (MA + MB)V
MAUA + MBUB = MAVA +MBVB
MAUA + MBUB = (MA+MB)V
Solution
- If the total force acting on a particle is zero, the linear momentum will be constant
This law states that for every action there is an equal and opposite reaction.
Application of Newtons Third law of motion are:
- Recoil of a gun
- Jet/rocket propulsion
- A person walking
When a bullet is fired from a gun, the gun moves backward with a velocity while the bullet moves forward with a velocity. Someone might ask but when a bullet leaves a gun, it moves forward with a greater speed than the backward movement of the gun, why is it so?
Answer: The reason is this, the gun has a greater mass compare to the bullet, so the bullet will move with a greater speed than the gun. At the end, the momentum of the gun and the bullet will be the same.
Backward movement of a gun = forward movement of bullet
-MGVG = MBVB
Example
- A rifle of mass 15kg fires a bullet of mass 60g with a velocity of 200m/s. calculate the recoil velocity of the rifle.
Solution
The fuel in the engine of a Jet/rocket undergoes combustion which releases a gas that propels the jet to move forward thereby obeying Newton’s third law of motion.
Example
- A rocket expels gas at the rate of 0.4kg/s. if the average force of the gas is 120N. Calculate the velocity of the gas
Solution
This principle state that if two bodies collide in a closed system, the total momentum before collision is equal to the total momentum after collision. The following steps can be use to understand this principle.
Step 1: When the two bodies are moving in the same direction before collision and after collision
MAUA + MBUB = MAVA + MBVB
Step 2: When the two bodies are moving in the same direction before collision and move in opposite direction after collision
MAUA + MBUB = MAVA - MBVB
Step 3: When two bodies are moving in the same direction and are moving as a unit after collision.
Where V is called the common velocity
Step 4: When one of the bodies is moving and the other is stationary
Where the initial velocity of B (UB) is zero since it is stationary.
Step 5: When one of the bodies is moving and the other is stationary
Question
- A body of mass 12kg travelling at 4.2m/s collides with a second body of mass 18kg at rest. Calculate their common velocity if the two bodies coalesce after collision.
This question can be solved by using step 5
When two bodies collide, we say collision has taken place. We have two types of collision
- Elastic Collision
- Inelastic Collision
Elastic Collision
In an Elastic Collision, the two bodies go their separate ways after collision. In this type of collision, the momentum before and after collision are the same i.e momentum is conserved. Also the kinetic energy before and after collision ate the same. Bear this at the back of your mind, there is no collision that is perfectly elastic.
Inelastic Collision
In an inelastic Collision, the two bodies move together as a unit after collision. Step 5 is an example of inelastic Collision. In this type of collision, the momentum is conserved but the kinetic energy before and after collision are not the same, this is because during collision, some of the energy is been converted to heat and sound energy.
Exercises
- A body(P) of mass 5kg moving with a velocity of 30m/s collides with another body(Q) moving in opposite direction with a velocity of 20m/s. if both bodies now move as a unit at a velocity of 10m/s. calculate the mass of Q
- A object of mass 1kg falls a distance of 5m onto a horizontal surface and bounces back to a vertical height of 2m. calculate the change in momentum
- A ball of mass 100g falls from a height of 5m onto a floor and rebounds to a height of 3m. What energy is lost as a result of the impact on the floor?
- Two bodies A and B of masses 4kg and 2kg move towards each other with velocities 3m/s and 2m/s and collide. If the collision is perfectly inelastic. Find the velocity of the two bodies after collision. Find the total kinetic energy of the system before and after collision. Hence calculate the loss in kinetic energy
- A 3kg rifle lays on a smooth table when it suddenly discharges, firing a bullet of 0.02kg with a speed of 500m/s. calculate the recoil speed of the rifle
- A bullet of mass 0.05kg is fired horizontally into a 10kg block which is free to move. If both bullet and the block move with velocity 0.5m/s after the impact. Find the velocity with which the bullet hit the body
- A rocket burns 0.01kg of fuel each second and ejects it as a gas with velocity of 5m/s. What force does the gas exert on the rocket?
- A jet engine develops a thrust of 270Ns when the velocity of the exhaust gases relative to the engine is 3000m/s. What is the mass of the material ejected per second?
- A lead bullet of mass 0.05kg is fired with a velocity of 200m/s into a lead block of mass 0.95kg. Given that the lead block can move freely, the final kinetic energy after impact is?
Solve the Exercises and write your answers in the comment section below