Linear momentum collision problem calculations 2

Questions 

1.     A toy truck with a mass of 3 kg was moving at 3 ms^-1 and hit with another toy truck of 1 kg and was moving with a velocity of 1 ms^-1, in the opposite direction. After collision, both trucks moved together in the same direction, calculate the common velocity of the two objects after collision.

 

m₁u₁ + m₂u_{2 =  (}m₁+ m₂₎v

            (3)(3) + (1)(-1) = (3+1)v

            9 – 1 = 4v

            v = 2 ms^-1

 

2.     A hunter shot a 100g bullet from a 1.5kg gun. If the bullet travelled 200 ms-1 after being triggered, what is the backward jerk of the gun. (Think final backward velocity of the gun).

 

Total initial momentum = Total final momentum = 0

m₁u₁ + m₂u_{2 =} 0

1.5(v) + 0.1(200) = 0 ß make sure to convert 100g to kg

1.5v +20 = 0

v = - 13.3 ms-1   ß Value is negative because gun moved in opposite direction

 

3.     A trolley of mass 2 kg was in a stationary condition, before a 5 g sticky plasticine was thrown into it with a velocity of 500 ms-1. After hitting the trolley, the plasticine sticks into it. Calculate the final velocity of both the trolley and plasticine?

Use the classic formula of momentum conservation

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

0.005 (500) + 2 (0) = (0.005+ 2)v

2.5 = 2.005v

 v = 1.245 ms^-1        

 

Analysing Momentum

Momentum

The momentum of an object is the product of its mass and its velocity.

p = m X v

The principles of conservation of liner momentum states that the total linear momentum of a closed system is constant.

The linear momentum before and after a collision is conserved if there is no external force acting on it.

Elastic collision: linear momentum, kinetic energy and total energy are conserved.

Inelastic collision: only linear momentum and total energy are conserved and there is a loss in kinetic energy.

In an EXPLOSION, where two objects move in opposite directions, the total linear momentum before and after the explosion is zero.

The acceleration of a rocket leaving the earth increases because:
a) its mass is decreasing.
b) air resistance is decreasing.
c) gravitational pull is decreasing.


Conservation of Momentum

1. The term conservation is derived from the root word “conserve” which means constant.
2. The principle of conservation of momentum states that in the absence of an external force, the total momentum of a system remains unchanged.
3. An example of external force is friction and this can be contact friction or air friction.
4. An isolated or closed system the sum of external forces is zero, thus, the principle of conservation of momentum is true for a closed system.

Collisions

1. There are two types of collision: 
(a) Elastic collision
(b) Inelastic collisions

2. In Elastic collision: Two objects collide and move apart again after a collision. Momentum is conserved. Total energy is conserved. Kinetic energy is conserved.
Formula: m1u1+m2u2 = m1v1+m2v2

Elastic Collision

3. In Inelastic collision: Two objects combine and stop or move together with a same velocity after a collision. Momentum is conserved. Total energy is conserved. Kinetic energy is not conserved (the total kinetic energy after the collision is less than the total kinetic energy before collision, excess energy is released as heat, sound energy etc).
Formula: m1u1+m2u2 = (m1+m2)v

Inelastic Collision