A box of mass
m = 59.0 kg
(initially at rest) is pushed a distance
d = 84.0 m
across a rough warehouse floor by an applied force of
FA = 204 N
directed at an angle of 30.0° below the horizontal. The coefficient of kinetic friction between the floor and the box is 0.100. Determine the following. (For parts (a) through (d), give your answer to the nearest multiple of 10.)
A) work done by the force of friction
B)Calculate the net work on the box by finding the sum of all the works done by each individual force.
C) Now find the net work by first finding the net force on the box, then finding the work done by this net force.
A) To determine the work done by the force of friction, we first need to understand the formula for work. Work (W) is defined as the dot product of the force vector (F) and the displacement vector (d). In this case, the force of friction opposes the motion, so the work done by friction is negative.
The formula for work is:
W = F * d * cos(theta),
where F is the magnitude of the force, d is the displacement, and theta is the angle between the force and the displacement vectors.
In this case, the force of friction (Ff) can be calculated using the formula:
Ff = coefficient of friction * normal force,
where the normal force (Fn) is equal to the weight of the box (mg), with g being the acceleration due to gravity. The normal force acts perpendicular to the surface.
Given values:
m = 59.0 kg (mass of the box)
g = 9.8 m/s^2 (acceleration due to gravity)
d = 84.0 m (displacement)
FA = 204 N (applied force)
theta = 30.0° (angle below the horizontal)
coefficient of kinetic friction (mu) = 0.100
To calculate the work done by the force of friction, we need to find the normal force, and then substitute the values into the work formula.
1. Find the normal force:
Fn = mg = 59.0 kg * 9.8 m/s^2
2. Calculate the force of friction:
Ff = mu * Fn
3. Determine the work done by the force of friction:
Wf = Ff * d * cos(theta)
Now, substitute the known values into the equations and calculate the results. Round the final answer to the nearest multiple of 10.
B) To find the net work on the box, we need to calculate the work done by each individual force and sum them together.
The work done by the applied force (FA) can be calculated using the same formula as before:
WFA = FA * d * cos(theta)
C) To find the net work by first calculating the net force on the box, we need to determine the horizontal component of the applied force and subtract the force of friction.
1. Calculate the horizontal component of the applied force:
FA_horizontal = FA * cos(theta)
2. Calculate the net force on the box (Fnet):
Fnet = FA_horizontal - Ff
3. Determine the net work by finding the work done by the net force:
Wnet = Fnet * d
Again, substitute the known values into the equations and calculate the results. Round the final answer to the nearest multiple of 10.
Please provide the values for mass, displacement, applied force, and angle so we can calculate the answers for each part.