Question

1.   During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a long barrel. What is the reason for using a long barrel in these guns?
2.   Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force?

3. A ball can be rolled down one of four different ramps, as shown below. The final elevation loss of each of the ramps is the same. Neglecting friction, for which ramp will the speed of the ball be the highest at the bottom?

4. A sled, initially at height h is sliding down an incline and then it continues moving on the horizontal plane until it stops. What's the energy required to drag it back up?
5. Three cars, Car X, Car Y, and Car Z, begin accelerating from rest, at the same time. Car X is more massive than Car Y, which is more massive than Car Z. The net force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum?
6. Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed of twice as high as Bill's ball. Compare the maximum heights in the two cases.
7. Particle 1 has 1/2 the mass of Particle 2, yet they both have the same kinetic energy. Compare the momenta of the two particles.

Answer 1

1) Rifles having long barrel causes forces to act longer on the bullets and hence tends to increase its speed but it cant be made very long because of losses due to friction and gravity acting

2)In 1st case,as momentum is conserved,both cars will return with 30mph & in 2nd case both car will move in same direction assuming elastic collision.So momentum loss in 1st case is more & so it will have larger impulse and thus larger impact force

3) figure not shown

4)E=mgh (m= mass of sled,g-gravity)

5) Car Z as it is lighter,it will have larger Accleration and hence larger speed

6)Hmax =V^2/2g

Vj =2Vb

So

Hj =4Hb (ans)

7) KE= P1^2/2m1 =P2^2/2m2

m1=m2/2

P1^2 =2P2^2

P1 = P2 sqrt2 (ans)

Answer 2

1. to allow the force of the expanding gases from the gunpowder to act for a longer time

2. the force would be same in both cases

3. A

5. they all have the same amount of momentum. If you use the equation p=mv and think about it carefully they all have different masses but have the same about of force, which means different velocity for each car. So, because car Z is most massive, then it has a small velocity. Car Y is in between. Car X is the lightest which means its mass will be small and the velocity will be high.

6.

Use conservation of energy:

For Bill 1/2 mv^2 = mgh ---> h = v^2/(2g)

Now let v --> 2v, then h --> h' = 2v^2/g

So Joe's ball travels 4 times hihger

7.