A 450 g steel ball rolls down an incline reaches a level surface and collides wi

Question

A 450 g steel ball rolls down an incline reaches a level surface and collides with a larger, 1.2 kg steel ball. Starting from rest, the ball travels 6.5 m along the incline before reaching the bottom. The incline makes an angle of 53 degrees above the horizontal. After the collision the smaller ball recoils and travels back 1.1 m along the track from the bottom of the incline. Air resistance and friction do no work on the balls. (Do NOT assume the collison was elastic!!)

(a) How fast is the lighter ball moving when it reaches the bottom of the incline?

(b) How fast is the heavier ball moving after the collision?

(c) What is the change in total mechanical energy (kinetic + potential) of the smaller ball before and after the collision?

(d) What is the change in mechanical energy of the larger ball before and after the collision.

(e) How much energy was lost in the collision?

Extra: (f) Find the speed of the larger ball and the distance the smaller ball travels back up the incline if the collision had been elastic.

Explanation / Answer

a) we can use energy for this. We first need to find the height to determine the energy of the light ball.
PE=mgh=mg6.5sin53=.45(9.8)6.5sin53
PE=22.893 joules
Now we set this energy to the kinetic energy at the bottom.
22.893=KE=(1/2)mv2    (i'm assuming no rotational energy because radii were not given)

v2=2(22.893)/.45

v=10.087 m/s

b)we first need to determine the velocity of the smaller ball once again using energy. The only difference is instead of 6.5m we will use 1.1m

v2=2(.45(9.8)1.1sin53)/.45

v=-4.150 m/s

Now we can use conservation of momentum

10.087(.45)=-4.150(.45)+1.2v

v=5.34 m/s

c)We already found the initial is 22.893 the final will be

E=mgh=.45(9.8)1.1sin53

E=3.8742 joules

Now we take the difference

E=3.8742-22.893

E=-19.02 joules

d)Initially the energy is 0. the final will be

E=(1/2)mv2=(1/2)(1.2)5.342

E=17.11

E=17.11 joules

e)To find how much energy was lost we find the total energy at start and subtract total energy at end.

E=22.893-(17.11+3.8742)
E=2.00 joules

Hope that helps

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.