A 54 kg box is being pushed a distance of 7.0 m across the floor by a force P whose magnitude is 153 N. The force P is parallel to the displacement of the box. The coefficient of kinetic friction is 0.25. Determine the work done on the box by FRICTIONAL FORCE.
Work = fricionforce*distance
= mu(mg)*distance.
thank you bob.
To determine the work done by the frictional force, we need to calculate the magnitude of the frictional force and then multiply it by the distance over which it acts.
First, we need to calculate the magnitude of the frictional force using the coefficient of kinetic friction. The frictional force can be calculated using the equation:
F_friction = μ * N
where μ is the coefficient of kinetic friction and N is the normal force.
The normal force can be calculated using the formula N = mg, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given:
Mass of the box (m): 54 kg
Coefficient of kinetic friction (μ): 0.25
Normal force (N) = mg = (54 kg) * (9.8 m/s^2)
Now we can calculate the frictional force (F_friction) using the formula F_friction = μ * N:
F_friction = (0.25) * (54 kg) * (9.8 m/s^2)
Next, we need to determine the displacement over which the frictional force acts. In this case, it is given as 7.0 m.
Finally, the work done by the frictional force can be calculated:
Work = F_friction * displacement
Plug in the values for F_friction and the displacement, and calculate:
Work = (F_friction) * (7.0 m)
To determine the work done on the box by the frictional force, we need to calculate the magnitude of the frictional force and multiply it by the displacement of the box.
The frictional force can be calculated using the formula:
Frictional force = coefficient of friction * normal force
The normal force is the force exerted by the floor on the box perpendicular to the surface, which is equal in magnitude to the weight of the box.
Weight = mass * acceleration due to gravity
Weight = 54 kg * 9.8 m/s²
The normal force is the same as the weight, but opposite in direction since it acts upwards:
Normal force = - (54 kg * 9.8 m/s²)
Substituting the given coefficient of kinetic friction into the frictional force equation:
Frictional force = 0.25 * Normal force
Next, we can calculate the magnitude of the frictional force by substituting the values we have found:
Frictional force = 0.25 * -(54 kg * 9.8 m/s²)
Now that we have the magnitude of the frictional force, we can calculate the work done by multiplying it by the displacement of the box:
Work = Frictional force * displacement
Substituting the given values into the equation:
Work = (0.25 * -(54 kg * 9.8 m/s²)) * 7.0 m
By evaluating this expression, we can find the work done on the box by the frictional force.