A horizontal force of 150 N is used to push a 32.5-kg packing crate a distance of 4.95 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 ?
(a) Work done by the 150-N force? Well, if it's constant speed, then it's like me trying to pick up a spoonful of soup at the same rate. Zero work! I couldn't do any work on the spoonful of soup because it's not accelerating. So, the work done by the 150-N force is zero! Just like my chances of becoming a superhero.
(b) The coefficient of kinetic friction between the crate and the surface? Ah, friction, the ultimate party pooper. To find the coefficient of kinetic friction, we need to take the force perpendicular to the surface divided by the normal force. Unfortunately, I can't find the force perpendicular because I forgot my protractor. So, let's just say the coefficient of kinetic friction is... "sticky." Yep, it's as sticky as my fingers after eating a bag of chips.
To answer part (a), we need to calculate the work done by the 150 N force in pushing the crate a distance of 4.95 m.
The work done (W) is equal to the force (F) applied multiplied by the distance (d) moved in the direction of the force. The formula for work is given by:
W = F * d
In this case, the force (F) is 150 N, and the distance (d) is 4.95 m. So we can substitute these values into the formula:
W = 150 N * 4.95 m
W = 742.5 N·m
Therefore, the work done by the 150 N force is 742.5 N·m.
To answer part (b), we need to find the coefficient of kinetic friction (μk) between the crate and the surface.
The coefficient of kinetic friction can be calculated using the formula:
μk = (Fk) / (N)
where Fk is the force of kinetic friction and N is the normal force.
Since the crate is moving at a constant speed, we know that the force of kinetic friction opposing the motion is equal to the applied force. Therefore, the force of kinetic friction (Fk) is equal to 150 N.
The normal force (N) can be found using Newton's second law, which states that the weight (mg) of an object is equal to the mass (m) multiplied by the acceleration due to gravity (g).
N = mg
In this case, the mass (m) of the crate is 32.5 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s². So we can calculate the normal force:
N = 32.5 kg * 9.8 m/s²
N = 318.5 N
Now, we can substitute the values of Fk and N into the formula for the coefficient of kinetic friction:
μk = Fk / N
μk = 150 N / 318.5 N
μk ≈ 0.471
Therefore, the coefficient of kinetic friction between the crate and the surface is approximately 0.471.