Projectiles, Collisions, Energy and Power problem set

Take g= 10m/s^-2

Give answers to 2 significant figures.

All formulas and calculations must be shown.

1. The graph shown below shows how force varies with time for a miniature crash test dummy of mass 2kg moving to the right. It is involved in a collision with a large concrete black set into the ground which brings it to rest.

a) Calculate the dummy’s speed just before hitting the block.

2.  A truck of mass 2500kg travelling at 20m/s^-1 west collides head on with a car of mass 800kg travelling in the opposite direction at 15m/s^-1. The two vehicles become locked together.

a)  What is the total momentum of the two vehicles before the collision? Assume the truck’s motion (west) is positive.

b)  What is the speed and direction of the car and truck immediately after the collision?

3.  A racing car negotiating a tight bend at 20km/h^-1 collides with a crash barrier. The air bag in his car inflates and the time taken for it to inflate is 0.16s. The driver’s head has a mass of 7.0kg. Explain why the driver is less likely to suffer head injury in a collsion with the air bag than if his head collided with the car dashboard, or other hard surface.

Three dot points required. These may be formulas, calculation, diagrams, explanations.

4.The graph below shows how total resistance forces acting on a cyclist and his bicycle vary with distance at the start of a race. The cyclist applies a constant force over the first 50meters of the race and travels at a constant velocity after travelling 40meters. The cyclist and bicycle have a combined mass of 80kg.

a)  How much work does the cyclist do against the resistance force over the first 40meters of the race?

b)  Calculate the power developed by the cyclist during the first 40meters of the race is he took 10 seconds to cover this distance.

c)  What was the magnitude of the constant force applied by the cyclist over the first 50meters of the race? (Answer + one dot-point required)

5.  A car is shown at the top of an extremely steep hill, of height 100m, as shown below. The mass of the car and driver is 1200kg. The car is at rest at point A.

a)  Assuming frictional forces are ignored, calculate the speed that the car has at point B if it is allowed to roll down the hill without the driver applying the brakes.

b)  Assuming the car applies the brakes and does 1.0×10^6J of work against friction as it rolls down the hill, what is the speed of the car at B now?

6.  The graph below shows how the force applied by a pinball spring plunger changes as it is compressed during a pinball game.

a)  The plunger is compressed 1cm and then released. If the pinball has a mass of 50grams, what is the speed at the instant it leaves the plunger?

7.  In a supermarket car park, a car of mass 1000kg collides with a loaded stationary supermarket trolley of mass 100kg. After the collision the car and supermarket trolley are held together by the car’s twisted bumper bar, and have a velocity of 10m/s. The duration of the impact was 20ms.

a)  What was the speed of the car before the collision?

b)  What is the average force exerted on the trolley by the car during the impact?

c)  This is ineleastic collision. Explain the meaning of the word ineleastic in this context, and show, using calculations, that the collision was inelastic.

8.  The ancient Egyptians used ramps to push limestone blocks with an average mass of 2300kg to heights of almost 150meters. The ramps were sloped at 10degrees to the horizontal. Friction was reduced by pumping water onto ramps.

a)  How much work would have been done to lift an average limestone block vertically through a height of 150meters?

b)  How much work would have to be done to push an average limestone block to the same height along a ramp inclined at 10degrees to the horizontal? Assume that friction is negligible.

c)  Explain how the inclined ramp helped to push the limestone.