Two crates, of mass m1 = 80 kg and m2 = 115 kg, are in contact and at rest on a horizontal surface. A 620 N force is exerted on the 80 kg crate. The coefficient of kinetic friction is 0.15.(a) Calculate the acceleration of the system.(b) Calculate the force that each crate exerts on the other.(c) Repeat with the crates reversed. How would I set this problem up?

Question

Two crates, of mass m1 = 80 kg and m2 = 115 kg, are in contact and at rest on a horizontal surface. A 620 N force is exerted on the 80 kg crate. The coefficient of kinetic friction is 0.15.(a) Calculate the acceleration of the system.(b) Calculate the force that each crate exerts on the other.(c) Repeat with the crates reversed. How would I set this problem up?

Answer 1

To set up this problem, we can first analyze the forces acting on the system.

(a) To calculate the acceleration of the system, we need to determine the net force acting on the system. In this case, the 620 N force is exerted on the 80 kg crate, and there is also friction acting on it. We can start by calculating the friction force on the 80 kg crate.

1. Calculate the friction force:
Friction force = coefficient of kinetic friction * normal force
Normal force = mass * gravity
Normal force = m1 * g

Since the two crates are in contact and at rest on a horizontal surface, the normal force acting on each crate is equal to the weight of the crate. Therefore, the normal force acting on the 80 kg crate is m1 * g, and g is the acceleration due to gravity.

Friction force = 0.15 * (m1 * g)

2. Calculate the net force on the 80 kg crate:
Net force = applied force - friction force
Net force = 620 N - friction force

3. Calculate the acceleration of the system:
Using Newton's second law (F = m * a), we can find the acceleration:
Net force = (m1 + m2) * a
620 N - friction force = (m1 + m2) * a

Now we can substitute the previous expressions to find the value of a:

620 N - 0.15 * (m1 * g) = (m1 + m2) * a

(b) To calculate the force that each crate exerts on the other, we can use Newton's third law, which states that for every action, there is an equal and opposite reaction. The force exerted by the 80 kg crate on the 115 kg crate will be equal in magnitude and opposite in direction to the force exerted by the 115 kg crate on the 80 kg crate.

(c) To repeat the calculations with the crates reversed, you would use the mass of the crates as m2 = 80 kg and m1 = 115 kg in the equations mentioned above.