Question

Two wooden crates rest on top of one another. The smaller top crate has a mass of m1 = 21 kg and the larger bottom crate has a mass of m2 = 90 kg. There is NO friction between the crate and the floor, but the coefficient of static friction between the two crates is μs = 0.8 and the coefficient of kinetic friction between the two crates is μk = 0.64. A massless rope is attached to the lower crate to pull it horizontally to the right (which should be considered the positive direction for this problem). 1)The rope is pulled with a tension T = 261 N (which is small enough that the top crate will not slide). What is the acceleration of the small crate? m

Answer 1

2.35 m/s²

Step-by-step explanation:

Given that

Mass of the smaller crate, m₁ = 21 kg

Mass of the larger crate, m₂ = 90 kg

Tensión of the rope, T = 261 N

We know that the sum of all forces for the two objects with a force of friction F and a tension T are:

(i) m₁a₁ = F

(ii) m₂a₂ = T - F, where m and a are the masses and accelerations respectively.

1) no sliding can also mean that:

a₁ = a₂ = a

This makes us merge the two equations written above together as:

m₂a = T - m₁a

If we then solve for a, we would have something like this

a = T / (m₁+m₂)

a = 261 / (21 + 90)

a = 261 / 111

a = 2.35 m/s²

Therefore, the needed acceleration of the small crate is 2.35 m/s²