Question

1.) A truck (mass 3549 kg) and a car (1957 kg) collide. The truck moves at a speed of 41 m/s towards the stationary car. Assuming this is an elastic collision, how fast will the truck be going after the collision? Answer as a whole number.

2.) A cylinder initially traveling at 3 m/s rolls up a hill inclined at 62 degrees. What is its vertical height when it comes to rest? Give your answer to one decimal place.

3.) A satellite rotates starting from rest for 4.0 seconds with an angular acceleration of 3.4 rad/s2. How many revolutions has the satellite undergone in this time interval? Your answer should have one decimal place.

Answer 1

Given,

mT = 3549 kg ; mC = 1957 kg ; vT = 41 m/s ;

since the target is at rest, the velocity of truck after collision will be:

vT' = (m1 - m2)vT/(m1 + m2)

vT' = (3549 - 1957)41/(3549 + 1957) = 11.85 m/s

Hence, vT' = 11.85 m/s

2)We know from conservation of energy

KE = PE

1/2 m v^2 = m g h

h = v^2/2g = 3^2/2 x 9.8 = 0.46 m

Hence, h = 0.5 m

c)alpha = 3.4 rad/s ; t = 4 s

We know that

theta = 1/2 alpha t^2

theta = 0.5 x 3.4 x 4^2 = 27.2 rad

N = theta/2 pi = 27.2/2 x 3.14 = 4.33 rev

Hence, N = 4.3 rev