Two crates, of mass 75 kg and 110 kg, are in contact and at rest on a horizontal surface. A 620-N force is exerted on the 75-kg crate. If the coefficient of kinetic friction is 0.15, calculate (a) the acceleration of the system, and (b) the force that each crate exerts on the other.
(c) Repeat with the crates reversed.
wondering if they are touching horizontally, or vertically.
they're touching horizontally
please help me :(
To solve this problem, we'll follow the steps:
(a) To calculate the acceleration of the system, we'll first determine the net force acting on the system using Newton's second law:
Net Force = Force applied - Frictional force
The force applied is given as 620 N, and the frictional force is determined by the coefficient of kinetic friction and the normal force.
Frictional force = coefficient of kinetic friction * Normal force
The normal force is the force exerted by the surface on the crates and is equal to the weight of the crates.
Normal force = mass * gravity
Where gravity is approximately 9.8 m/s^2.
Let's calculate the acceleration of the system now.
Mass of crate 1 (75 kg): m1 = 75 kg
Mass of crate 2 (110 kg): m2 = 110 kg
Force applied: F = 620 N
Coefficient of kinetic friction: μ = 0.15
Gravity: g = 9.8 m/s^2
Step 1: Calculate the normal force:
Normal force = (m1 + m2) * g
Step 2: Calculate the frictional force:
Frictional force = μ * Normal force
Step 3: Calculate the net force:
Net force = F - Frictional force
Step 4: Calculate the acceleration:
Acceleration = Net force / (m1 + m2)
Let's substitute the values and calculate the acceleration.
Normal force = (75 kg + 110 kg) * 9.8 m/s^2
Normal force = 185 kg * 9.8 m/s^2
Frictional force = 0.15 * (185 kg * 9.8 m/s^2)
Net force = 620 N - Frictional force
Acceleration = Net force / (75 kg + 110 kg)
(b) The force that each crate exerts on the other is equal in magnitude but opposite in direction. Let's calculate the force exerted by each crate.
Force exerted by crate 1 on crate 2 = m1 * acceleration
Force exerted by crate 2 on crate 1 = m2 * acceleration
Let's substitute the values and calculate the forces.
(c) To repeat with the crates reversed, we'll exchange the masses of the crates.
Mass of crate 1 (110 kg): m1 = 110 kg
Mass of crate 2 (75 kg): m2 = 75 kg
Repeating the steps mentioned in (a) and (b), we can calculate the acceleration and the forces exerted by each crate.
Please provide the values of m1, m2, F, and μ, and I'll calculate the results for you.