Question

Two students are pushing identical crates across a frictionless floor. The crates are initially at rest. Bing applies a horizontal force of 19 N to his crate. Bob, who is shorter than Bing, pushes on his crate at an angle of 33° below the horizontal, also with a force of 19 N. Find the ratio of the masses of the two crates if Bing’s crate is moving at twice the speed of Bob’s crate after they have traveled a distance of 33.5 m across the floor? (20 pts) SHOW YOUR WORK.

Answer 1

Let Bing be denoted as 1 and Bob be denoted as 2

For Bing,

F1 = 19 N

so,

a1 = 19 / m1

For Bob

F2 = 19 * cos 33

so,

a2 = 19*cos 33 / m2

Also,

v1 = 2*v2

we know that work done = change in kinetic energy

as box was at rest initially, so initial kinetic energy is zero.

so,

F*d = 1/2mv²

as distance moved is same

19 * d / 19 * cos 33 * d = m1 * (2 v2)² / m2 * v2²

1 / cos 33 = m1 * 4 * v2² / m2 * v2²

1 / cos 33 = m1 * 4 / m2

m2 = m1 * 4 * cos 33

m2 / m1 = 3.354

OR

m1 / m2 = 0.298