Final answer:
To determine the maximum force that can be exerted on the crate without moving it, use the equation F_s = μ_s * N, and calculate the maximum static friction force. Once the crate starts to slip, the force of friction changes to the force of kinetic friction, which can be calculated using F_k = μ_k * N. The acceleration of the crate when it starts to slip can be calculated using the equation a = F_k / m.
Step-by-step explanation:
To determine the maximum force that can be exerted on the crate without moving it, we need to consider the static friction between the crate and the floor. The maximum force of static friction can be calculated using the equation F_s = μ_s * N, where F_s is the force of static friction, μ_s is the coefficient of static friction, and N is the normal force. Since the crate is on a horizontal floor, the normal force is equal to the weight of the crate, which can be calculated as N = m * g, where m is the mass of the crate and g is the acceleration due to gravity.
Once the crate starts to slip, the force of friction changes to the force of kinetic friction which is given by F_k = μ_k * N. The coefficient of kinetic friction is usually less than the coefficient of static friction, so the force of kinetic friction is less than the maximum static friction force. The acceleration of the crate can be calculated using the equation a = F_k / m.
Let's calculate the maximum force of static friction and the acceleration of the crate when it starts to slip:
a) Using the given mass of 120 kg, the force of static friction can be calculated as F_s = (0.5) * (120 kg * 9.8 m/s^2) = 588 N.
b) Once the crate starts to slip, the force of kinetic friction is given as F_k = (0.4) * (120 kg * 9.8 m/s^2) = 470.4 N. The acceleration of the crate can be calculated as a = F_k / m = 470.4 N / 120 kg = 3.92 m/s^2.