MOMENTUM AND COLLISION
1. Define the term
(i) Momentum (1mk)
It is the product
... [Show More] of mass and velocity of a body
(ii) Inelastic collisions (1mk)
These are the collisions where the colliding bodies do not separate after collision. Momentum is conserved while kinetic energy is not conserved
(iii) Elastic collisions (1mk) These are the collisions where the bodies separate after collision. Both momentum and kinetic energy are conserved
2. State why energy is not conserved during an inelastic collision. (1mk)
Energy is lost in form of sound, light and heat. Energy is also used as the bodies get deformed.
3. Give one example of an inelastic collision. (1mk)
A bullet fired to a tree gets stuck to the trunk
Plasticine thrown and sticks to a surface
A monkey jumping on a branch and swings on the branch as soon as it lands on the branch
4. State the principle of conservation of linear momentum. (1mk) For a system of colliding bodies, the total linear momentum is conserved provided no external forces act.
5. State the law of conservation of energy. (1mk)
Energy can neither be created nor destroyed but can only be transformed from one form to another.
6. A motor cyclist wears a helmet in the inside with sponge. Explain how this minimizes injuries to the motorist’s head when involved in an accident. (2mk) The sponge in the helmet acts as a shock absorber. It increases the time of impulse and reducing the effect of the impulsive force or help spread the impact over a long time.
7. A trolley is moving at constant speed in a friction compensated track. Some plasticine is dropped on the trolley and sticks to it. State with a reason what is observed about the motion of the trolley.
The speed of the trolley decreases. Since momentum is conserved an increase in mass (plasticine) implied a decrease in velocity.
8. A trolley is moving at uniform speed along a straight horizontal path. A piece of plasticine is dropped on the trolley and sticks on it. State and explain the resultant motion of the trolley. (2mks)
The speed of the trolley decreases. Since the trolley is on a frictional surface, the speed decreases and the trolley may come to a stop. The increase in mass decreases the time taken to reduce the speed.
9. A cyclist carrying two bags of maize tied a cross back seat is traveling at uniform velocity. The bags suddenly fall. If the bags do not touch the back wheel explain what happens? (2mks) The cyclist moves faster. This is because the total mass of the body is reduced and since momentum is conserved the speed of the cyclist increases.
10. Explain why a high jumper flexes his knees when landing on the ground.
(2mk)
To increase the time taken to land. When time is increased the force of impact is reduced making the jumper to land safely.
11. Explain why unboiled egg stops faster than a boiled egg when both are rolled together on a flat horizontal surface with same velocity. (2mks) The unboiled egg experiences a more retarding force due to the liquid hence slowing the egg faster. The boiled egg experiences less retarding force since it is solid.
12. A high jumper usually lands on a thick soft mattress. Explain how the mattress helps in reducing the force of impact.
The mattress increases the time taken to land. This is to increase the reaction time and hence reduce the impulsive force acting on the jumper.
13. A parachutist allows his legs to bend and rolls over on the ground when he lands. Explain. (2mk)
The bending of legs increases the time o impact thus reducing the effect of force of impact. (If they hit the ground stiff-legged, then their speed goes to zero very quickly and they can get hurt)
14. A modem car with a strengthened passenger cage has regions at the front and the back which can collapse in a crash.
Explain how the collapsible regions should reduce passenger injury in a car
crash. (3mks)
The collapsible regions increase the time taken for the change in momentum to take place. On collision they collapse increasing the time of impact. This reduces the rate of change of momentum of the passengers, thus force f impact is reduced.
15. Two identical cans A and B are suspended from a horizontal support with strings of the same length as shown in Fig.4.Can A is empty while B is full of paint.
They are both displaced simultaneously and left to swing freely. Which can is likely to remain swinging for a longer time? Explain. (2mks) Can A will continue swinging for a longer time than can B. This is because can B will have a greater reduction in momentum since it has more mass and force is constant for both.
16. A particle A of mass m moving with an initial velocity u m/s makes a head on collusion with another particle B of mass 2m kg at rest. In terms of u express the final velocity V of the two if the collusion is perfectly inelastic.
3mk
mu1 1 m u2 2 (m m v1 2) mu(2m*0) (m 2 )m v
vu3m s/
17. A bullet of mass 40g is fired at a velocity of 400ms-1 from a gun of mass 8kg. Determine the corresponding velocity of the gun. (2mk)
0 mv1 1 m v2 2
40
*400 8v
1000 v2m s/
The recoil velocity is 2 m/s or the velocity of the gun is -2 m/s
18. A bullet of mass 0.006kg is fired from a gun of mass 0.5kg. If the muzzle velocity of the bullet is 300m/s. calculate the recoil velocity of the gun. 3mk
mu1 1 m v2 2
0.006*300 0.5v2 v2 3.6m s/
The recoil velocity is 3.6 m/s
19. Calculate the recoil velocity of a gun of mass 0.4kg which fires a bullet of mass 0.0045kg at a velocity of 400ms-1 (3mk)
mu1 1 m v2 2
0.0045*400 0.4v2 v2 4.5m s/
The recoil velocity is 4.5 m/s
20. A car of mass 800kg starts from the rest and accelerates at 1.2ms-2. Determine its momentum after it has moved 400m from the starting
v2 u2 2as v2 0 (2*1.2*400) v 30.98m s/
momentum mv
P 800*30.98
P 24784kgm s/
21. Two bodies of masses 5kg and 8 kg moving in the same direction with velocities 20m/s and 15m/s respectively collide in elastically. Determine the velocity of the bodies after collision. (3mk)
mu1 1 m u2 2 (m1 m v2) (5*20)(8*15) (5 8)v v16.92m s/
22. A bullet of mass 20g moving with a velocity of 1000m/s hits stationery antelope of mass 12kg.The bullet embeds and the two moves in one direction. Calculate its final velocity (2mk)
mu1 1 m u2 2 (m1 m v2)
( *1000) (12*0) (0.0212)v v1.664m s/
23. A bullet of mass 22g traveling horizontally with a velocity of 300ms-1 strikes a block of wood of mass 1,978g which rests on a rough horizontal surface. After impact the bullet and the block move together and come to rest when the block has traveled a distance of 5m. Calculate:
(i) The velocity of bullet and wood after impact. (2mks)
mu1 1 m u2 2 (m1 m v2)
(1000 22 *300)(10001978 *0) ( 2210001978)v v 3.3m s/
(ii) The force of friction between wood and surface. (2mks)
v2 u2 2as
3.32 0 (2 *5)a a1.089
F ma
*1.089
2.154N
24. A cyclist of mass 200kg and traveling at 90km/h is involved in a head on collision with a car of mass 600 kg traveling at 110km/h. The cyclist is thrown onto the bonnet of the car which continued to move after impact in the original direction. Find their velocity after impact (3mks)
u1 90km h/ 25m s/ u2 110km h/ 30.56m s/
mu1 1 m u2 2 (m m v1 2)
(200*25)(600* 30.56) (200 600)v v16.67m s/
25. An arrow of mass 20g traveling horizontally strikes a block of wood of mass 1980g resting on a horizontal surface. The impact takes 0.2 s before the two move together with an initial velocity of 5m/s. Calculate:
(i) The velocity of the arrow before the impact [Show Less]