A horizontal force of 150 N is used to push a 43.5 kg packing crate a distance of 5.30 m on a rough horizontal surface. If the crate moves at constant speed, find each of the following.

(a) the work done by the 150 N force


(b) the coefficient of kinetic friction between the crate and the surface

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To find the answers to the given questions, we need to use the concepts of work and kinetic friction. Let's tackle each question step by step:

(a) The work done by the 150 N force:
Work is defined as the product of force and displacement in the direction of the force. In this case, the force applied is 150 N, and the displacement is 5.30 m. Since the crate moves at a constant speed, this means that the net force acting on the crate is zero (as the applied force is balanced by the force of friction). Therefore, the work done by the applied force is zero, because work is only done when there is a net force acting in the direction of displacement.

So, the answer is zero.

(b) The coefficient of kinetic friction between the crate and the surface:
The coefficient of kinetic friction can be found by relating the force of friction to the normal force between the crate and the surface. Since the crate is on a rough horizontal surface and moving at a constant speed, we know that the force of friction is equal in magnitude but opposite in direction to the applied force (150 N). Therefore, the force of friction can be calculated as the product of the normal force (equal to the weight of the crate) and the coefficient of kinetic friction (µk).

The weight of the crate can be found using the formula: weight = mass × acceleration due to gravity. Given that the mass of the crate is 43.5 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:

Weight = mass × acceleration due to gravity
Weight = 43.5 kg × 9.8 m/s^2
Weight ≈ 426.3 N

Now, we can set up the equation for the force of friction:

Force of friction = coefficient of kinetic friction × normal force
150 N = µk × 426.3 N

Now, we can solve for the coefficient of kinetic friction (µk):

µk = 150 N / 426.3 N
µk ≈ 0.352

So, the coefficient of kinetic friction between the crate and the surface is approximately 0.352.

In summary:
(a) The work done by the 150 N force is zero.
(b) The coefficient of kinetic friction between the crate and the surface is approximately 0.352.