The coefficient of kinetic friction between a 50-kg crate and the ground is [tex]\mu_k = 0.3[/tex]. The crate starts from rest, and a force of [tex]P = 215 \, \text{N}[/tex] is applied to it. What is the acceleration of the crate?

To find the acceleration of the crate, we can use Newton's second law of motion and calculate the net force. The acceleration of the crate is approximately 1.77 m/s^2.

Explanation:

To find the acceleration of the crate, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the applied force is 215 N, and the mass of the crate is 50 kg. The net force also includes the force of friction, which can be calculated using the coefficient of kinetic friction and the normal force. The normal force is equal to the weight of the crate, which is the mass of the crate multiplied by the acceleration due to gravity. So, the equation for the net force is

Fnet = ma = P - μkN = P - μkmg

where μk is the coefficient of kinetic friction, N is the normal force, and g is the acceleration due to gravity. Rearranging the equation to solve for acceleration:

a = (P - μkmg) / m

Substituting the given values:

a = (215 N - 0.3 * 50 kg * 9.8 m/s^2) / 50 kg

a ≈ 1.77 m/s^2

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