A 280 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 6.00 m.
(a) Find the work done by the pulling force.
(b) Find the work done by the kinetic frictional force.
J
To find the work done by the pulling force and the work done by the kinetic frictional force, we first need to find the net force acting on the refrigerator.
1. Resolve the pulling force into its horizontal and vertical components:
F_horizontal = F * cos(θ)
F_vertical = F * sin(θ)
Substituting the given values:
F_horizontal = 280 N * cos(18°) = 263.75 N
F_vertical = 280 N * sin(18°) = 88.99 N
2. Calculate the normal force acting on the refrigerator:
The vertical component of the pulling force balances the weight of the refrigerator, so the normal force is equal to the weight:
Normal force (N) = m * g
Substituting the given values:
N = 80.0 kg * 9.8 m/s^2 = 784 N
3. Calculate the frictional force:
The frictional force (F_friction) is given by:
F_friction = μ * N
Substituting the given values:
F_friction = 0.200 * 784 N = 156.8 N
4. Calculate the net force:
The net force is the vector sum of the horizontal component of the pulling force and the frictional force:
Net force = F_horizontal - F_friction
Substituting the calculated values:
Net force = 263.75 N - 156.8 N = 106.95 N
(a) Find the work done by the pulling force:
The work done by a force is given by the dot product of the force and the displacement vector:
Work (W) = F * d * cos(θ)
Substituting the given values:
W = 280 N * 6.00 m * cos(18°) = 1512 J
(b) Find the work done by the kinetic frictional force:
The frictional force acts in the opposite direction to the displacement, so the work done by the frictional force is negative:
Work (W) = -F_friction * d
Substituting the calculated values:
W = -156.8 N * 6.00 m = -940.8 J
Therefore,
(a) The work done by the pulling force is 1512 J.
(b) The work done by the kinetic frictional force is -940.8 J.
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 done.
(a) The work done by a force is given by the formula:
Work = Force x Distance x Cosine(angle)
In this case, the force pulling the refrigerator is 280 N, and the angle between the force and the displacement is 18.0°. The distance the refrigerator moves is 6.00 m. Plugging these values into the formula:
Work = 280 N x 6.00 m x Cos(18.0°)
Now we can calculate the work done by the pulling force.
(b) The work done by the kinetic frictional force can be calculated using the formula:
Work = Force of friction x Distance
To find the force of friction, we need to multiply the normal force by the coefficient of kinetic friction. The normal force is equal to the weight of the refrigerator, which can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
The mass of the refrigerator is 80.0 kg, and the acceleration due to gravity is approximately 9.8 m/s². Plugging these values into the formula for weight:
Weight = 80.0 kg x 9.8 m/s²
Once we have calculated the weight, we can use it to find the force of friction. The force of friction is equal to the weight multiplied by the coefficient of kinetic friction, which is given as 0.200. Plugging in the values:
Force of friction = Weight x Coefficient of kinetic friction
Now that we have the force of friction, we can calculate the work done by multiplication with the distance the refrigerator moves:
Work = Force of friction x Distance
Now we can calculate the work done by the kinetic frictional force.
Finally, we can provide the answers to each part of the question.