Momentum 1:- Example

Note: This is an example sheet with solutions and is not regenerating.

Momentum 1

1. A car of mass 1 tonne is travelling at 5 ms-1 south. What is its momentum?

2. A 500g linear air track glider A was travelling to the right at 0.2 ms-1 when it collided with an identical linear air track glider B travelling to the left at the same speed. After the collision the two gliders recoiled (bounced back) at the same speed.
(i) What was the momentum of glider A before the collision?
(ii) What was the total momentum of the system (glider A + glider B) before the collision?
(iii) What was the momentum of glider A after the collision?
(iv) What was the change of momentum of glider B due to the collision?

3. A 1500kg car travelling east slowed to 40 km/h as it entered a school zone. A 3 tonne truck travelling at 60 km/h failed to slow down and collided with the rear of the car. The vehicles coalesced (joined together) during the collision.
What was the speed of the truck + car after the collision?

4. A force of 500N west was applied to a car of mass 1800kg for 1 minute.
(i) What was the change in momentum of the car?
(ii) If the initial speed of the car was zero, what was the velocity of the car after the force had been applied.
(iii) What was the acceleration of the car over the minute the force was being applied?

5. A 400g linear air track glider A was travelling to the right at 0.4 ms-1 when it collided with a 600g linear air track glider B travelling to the left at 0.5 ms-1. After the collision the Glider A recoiled (bounced back) at 0.6 ms-1.
(i) What was the momentum of glider B before the collision?
(ii) What was the total momentum of the system (glider A + glider B) before the collision?
(iii) What was the momentum of glider A after the collision?
(iv) What was the momentum of glider B after the collision?
(v) What was the change in momentum for glider A?
(vi) What was the change in momentum for glider B?

6. A car of mass 2200kg is travelling north at 72km/h and comes to a bend in the road. Twenty seconds later it is travelling east at 72 km/h.
What is the change in momentum of the car?

Answers: Momentum

1. A car of mass 1 tonne is travelling at 5 ms-1 south. What is its momentum?
p = mv p = 1000 x 5 = 5000kgms-1 or 5000Ns (note; 1 tonne = 1000 kg)

2. A 500g linear air track glider A was travelling to the right at 0.2 ms-1 when it collided with an identical linear air track glider B travelling to the left at the same speed. After the collision the two gliders recoiled (bounced back) at the same speed.

(i) What was the momentum of glider A before the collision?
p = mv = 0.5 x 0.2 = 0.1 Ns right.
(ii) What was the total momentum of the system (glider A + glider B) before the collision? Momentum of glider A = 0.1Ns right Momentum of glider B = 0.1Ns left
Let right be positive (+ 0.1Ns) + (- 0.1Ns) = 0Ns OR Let left be positive (- 0.1Ns) + (+ 0.1Ns) = 0Ns (iii) What was the momentum of glider A after the collision?
Since the gliders recoiled the Glider A was travelling at 0.2 ms-1 to the left after the collision.
p = mv = 0.5 x 0.2 = 0.1 Ns left.
(iv) What was the change of momentum of glider B due to the collision?
Change inmomentum = final momentum - initial momentum Let right be positive (-0.1 ) - (0.1) = -0.2 p = -0.2Ns i.e. 0.2 Ns to the left OR Let left be positive (0.1 ) - ( -0.1) = 0.2 Δp = +0.2Ns i.e. 0.2 Ns to the left

3. A 1500kg car travelling east slowed to 40 km/h as it entered a school zone.
A 3 tonne truck travelling at 60 km/h failed to slow down and collided with the rear of the car. The vehicles coalesced (joined together) during the collision.
What was the speed of the truck + car after the collision?

40 km/h = (40x1000) /(60x 60) m/s = 11.1111m/s
60 km/h = (60x1000) /(60x 60) m/s = 16.6667m/s
Momentum of car before collision = mv = 1500 x 11.1111 = 16666.5 Ns
Momentum of truck before collision = mv = 1500 x 16.6667= 25000Ns
Total momentum before collision = 25000 + 16667 = 41667 Ns east
Momentum is conserved so total momentum after collision = 41667 Ns east
Mass of car + truck = 1500 + 3000 = 4500kg
Speed after collision = 41667/4500 = 9.26 m/s = (9.26 x60 x 60)/1000 km/h = 33.33 km/h
Speed of car + truck = 9.26 m/s or 33.33 km/h

We can also solve the problem without using SI units.
Momentum of car before collision = mv = 1500 x 40 = 60 000 kgkm/h  
Momentum of truck before collision = mv = 1500 x 60 = 90 000 kgkm/h  
Total momentum before collision = 60000 + 90000 = 150 000 kgkm/h east
Momentum is conserved so total momentum after collision = 150 000 kgkm/h east
Mass of car + truck = 1500 + 3000 = 4500kg
Speed after collision = 150000/4500 = 33.33 km/h = (33.33 x 1000)/ (60 x 60) = 9.26 m/s
Speed of car + truck = 9.26 m/s or 33.33 km/h

4. A force of 500N west was applied to a car of mass 1800kg for 1 minute.
(i) What was the change in momentum of the car?
Change of momentum = impulse = Ft =500 x 60 = 30 000Ns west
(ii) If the initial speed of the car was zero, what was the velocity of the car after the force had been applied.
mv = 1800v = 30000 v = 30000/1800 = 16.66667m/s west
(iii) What was the acceleration of the car over the minute the force was being applied?
a = Δv /Δt = 16.66667/60 = 0.2778 ms-2 west

5. A 400g linear air track glider A was travelling to the right at 0.4 ms-1 when it collided with a 600g linear air track glider B travelling to the left at 0.5 ms-1. After the collision the Glider A recoiled (bounced back) at 0.6 ms-1.

(i) What was the momentum of glider B before the collision?
p = mv = 0.6 x 0.5 = 0.3 kgm/s left = 0.3 Ns left
(ii) What was the total momentum of the system (glider A + glider B) before the collision?
momentum = 0.4 x 0.4 Ns right + 0.3Ns left = 0.16Ns right + 0.3 Ns left = 0.14Ns left
(iii) What was the momentum of glider A after the collision?
p = mv = 0.4 x 0.6 = 0.24 Ns left
(iv) What was the momentum of glider B after the collision?
0.14 Ns left - 0.24 Ns left = - 0.10 Ns left = 0.1Ns right
(v) What was the change in momentum for glider A?
Change in momentum = final momentum - initial momentum
Δp = 0.4 x 0.6 (left) - 0.4 x 0.4 (right)
To subtract vectors, add the opposite
Δp= 0.24 Ns left + 0.16Ns left = 0.40Ns left
(vi) What was the change in momentum for glider B?
Momentum of glider B before collision = 0.6 x 0.5 = 0.3 Ns left
Momentum of glider B after collision = 0.1 Ns right (part iv)
Change in momentum = final momentum - initial momentum
Δp= 0.1 Ns right - 0.3Ns left = 0.1Ns right + 0.3 Ns right = 0.40Ns Right

NOTE THAT THE CHANGE IN MOMENTUM OF GLIDER A IS EQUAL AND OPPOSITE TO THE CHANGE IN MOMENTUM OF GLIDER B

6. A car of mass 2200kg is travelling north at 72km/h and comes to a bend in the road. Twenty seconds later it is travelling east at 72 km/h.
What is the change in momentum of the car?

72 km/h= (72 x 1000)/(60 x 60) = 20m/s
Initial momentum = 2200 x 20 = 44000 Ns north
Final momentum = 2200 x 20 = 44000 Ns east
Change in momentum = final momentum - initial momentum
To subtract a vector add the opposite.
44000Ns east - 44000Ns north = 44000 Ns east + 44000Ns south

R2 = 440002 + 440002 = 3872000000
R = √(3872000000) = 62 225 Ns South East