A 4-kg box is pushed to the right by a force of 2 N for a distance of 9 m. It ha
ID: 1785431 • Letter: A
Question
A 4-kg box is pushed to the right by a force of 2 N for a distance of 9 m. It has an initial velocity of 4 m/s to the right. NOTE: Since this problem gives the DISTANCE x traveled, FIRST look at kinetic energy and calculate the NET WORK using Wnet = F x = K. After the kinetic energy values are calculated, then calculate the momenta and impulse values. Remember that on quiz and test problems, you will need to decide which values should be calculated first.
What is the initial momentum pi of the box?
16 kg m/s
What is the impulse or change in momentum p of the box?
____kg m/s
What is the final momentum pf of the box?
____kg m/s
What is the initial kinetic energy Ki of the box?
32 J
What is the change in kinetic energy K of the box?
18 J
What is the final kinetic energy Kf of the box?
____J
How long t does it take for the box to travel the distance of 9 m?
____s
Explanation / Answer
initial kinetic energy ki = 1/2mvi^2 = 1/2*4*4^2 = 32 J
a = f/m = 2/4 = 0.5 m/s^2
vf^2 = vi^2+2ad
vf = sqrt(4^2+2*0.5*9) = 5 m/s
final kinetic energy kf = 1/2*4*5^2 = 50 J
change in kinetic energy = 50-32 = 18 J
initial momentum = m*vi = 16 kg m/s
final momentum = m*vf = 4*5 = 20 kg m/s
change in momentum = 20-16 = 4 kg m/s
change in moemntum = impulse = f*time
time = 4/2 = 2 sec