Final answer:
The coefficient of kinetic friction between a 780 Newton crate is 0.4. Thus the correct option is (b).
Step-by-step explanation:
The coefficient of kinetic friction (μk) is a measure of the resistance to motion between two surfaces in contact when one is moving relative to the other. In this case, we are concerned with the friction between a crate and the surface it is resting on. To determine the coefficient of kinetic friction, we need to know the force of friction (Ff) and the normal force (N) acting on the crate. The normal force is the force perpendicular to the surface that the crate is resting on, and it is equal to the weight of the crate divided by the acceleration due to gravity (g). Thus the correct option is (b).
Let's say the weight of the crate is 780 Newtons (N), and g is 9.8 m/s². We can calculate the normal force as follows:
N = 780 N / 9.8 m/s² = 80 N
Now, let's assume that the crate is being pulled across a surface with a constant acceleration (a). The force required to overcome friction and accelerate the crate is equal to the product of its mass (m), acceleration (a), and coefficient of kinetic friction (μk). Therefore, we can write:
Ff = m * a * μk
Since we know that Ff = N * μk, we can substitute this expression into our equation for Ff and solve for μk:
N * μk = m * a * μk
μk = m * a / N
Using our values for m, a, and N, we can calculate the coefficient of kinetic friction:
μk = 780 kg * 2 m/s² / 80 N = 0.4
Therefore, the coefficient of kinetic friction between our 780 Newton crate and the surface it is resting on is approximately 0.4. This value will remain constant as long as there are no changes in the materials or conditions involved in this interaction.