A 3.00 102 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 the pulling force and the work done by the kinetic frictional force, we need to use the formulas for work. The work done by a force is given by the equation:
Work = Force * Distance * cosine(theta)
where Force is the magnitude of the force, Distance is the displacement of the object, and theta is the angle between the force and the direction of displacement.
(a) To find the work done by the pulling force, we have the magnitude of the force (3.00 * 10^2 N) and the angle between the force and the displacement (18.0°). The distance covered by the refrigerator is given as 8.00 m.
First, we need to find the horizontal component of the pulling force. The horizontal component can be found by multiplying the magnitude of the force by the cosine of the angle:
Horizontal component of the pulling force = 3.00 * 10^2 N * cos(18.0°).
Next, we can calculate the work done by the pulling force using the formula:
Work = Horizontal component of the pulling force * Distance.
Plugging in the values, we get:
Work = (3.00 * 10^2 N * cos(18.0°)) * 8.00 m.
Solving this equation will give us the work done by the pulling force.
(b) To find the work done by the kinetic frictional force, we need to use the coefficient of kinetic friction and the normal force.
The normal force is equal to the weight of the refrigerator, which can be found using the formula:
Weight = mass * gravitational acceleration,
where mass is given as 80.0 kg and the gravitational acceleration is approximately 9.8 m/s^2.
Next, we can calculate the magnitude of the frictional force using the formula:
Frictional force = coefficient of kinetic friction * normal force.
Finally, we can find the work done by the kinetic frictional force using the formula:
Work = Frictional force * Distance.
Substituting the values, we can solve this equation to find the work done by the kinetic frictional force.
Note: The direction of the work done by the kinetic frictional force is opposite to the direction of displacement, so the work done by the kinetic frictional force will be negative.