A 3.00*10^2 N force is pulling an 80.0 kg refrigerator across a horizontal surface. The force acts at an angle of 18.0° above the surface. The coefficient of kinetic friction is 0.200, and the refrigerator moves a distance of 8.00 m.
(a) Find the work done by the pulling force.
(b) Find the work done by the kinetic frictional force.
To find the work done by a force, we use the formula:
Work = Force * Distance * Cos(θ)
where:
- Work is the work done by the force,
- Force is the applied force,
- Distance is the distance over which the force is applied,
- θ is the angle between the force and the direction of displacement.
(a) Find the work done by the pulling force:
The given force is 3.00 * 10^2 N, and the distance is 8.00 m. The angle between the force and displacement is 18.0°. Plugging these values into the formula, we get:
Work = 3.00 * 10^2 N * 8.00 m * Cos(18.0°)
To get the numerical value, calculate Cos(18.0°), multiply it by 3.00 * 10^2 N, and then multiply the result by 8.00 m.
(b) Find the work done by the kinetic frictional force:
The work done by the kinetic frictional force can be found using the same formula:
Work = Force * Distance * Cos(θ)
The force of kinetic friction can be calculated using the formula:
Force of friction = Coefficient of friction * Normal force
where the normal force is equal to the weight of the refrigerator, which can be found using the formula:
Normal force = mass * gravitational acceleration
Given that the mass of the refrigerator is 80.0 kg, the gravitational acceleration is 9.8 m/s^2. Once the normal force is calculated, multiply it by the coefficient of kinetic friction to find the force of friction. Finally, multiply the force of friction by the distance over which it acts, and calculate the cosine of the angle between the force of friction and the displacement.
Work = Force of friction * Distance * Cos(θ)
Substitute the calculated force of friction and the given values to solve for the work done by the kinetic frictional force.