carol and bruno drag a box of mass 58.0 kg along a frictionless floor. Carol pushes the box with a force of 11.4 N at an angle of 40.0 downward from the horizontal. Bruno pulls the box from the other side with a force of 11.0 N at an angle of 40.0 above the horizontal. What is the net work done on the box if the displacement of the box is 14.5 m?
A. 5.8 J
B. 2.49 10^2 J
C. 3.25 10^2 J
D. 8.24 10^3 J
I know the formula is W=Fdcos0 but I keep trying and can't get the right answer
You have to add the F d cos theta values of both Carol and Bruno.
14.5 m * (11.4 cos 40 + 11.0 cos 40)Newtons
= 249 J
To calculate the net work done on the box, we need to find the work done by both Carol and Bruno, and then sum them up.
The formula to calculate work is: W = F * d * cosθ, where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the displacement.
1. For Carol's force:
Given force F1 = 11.4 N
Given angle θ1 = 40.0° downward from the horizontal
Given displacement d = 14.5 m
To calculate the work done by Carol's force, we can substitute these values into the work formula:
W1 = F1 * d * cosθ1
W1 = 11.4 N * 14.5 m * cos(40.0°)
2. For Bruno's force:
Given force F2 = 11.0 N
Given angle θ2 = 40.0° above the horizontal
To calculate the work done by Bruno's force, we also need the horizontal displacement, as Bruno's force is at an angle above the horizontal. We can calculate the horizontal displacement using trigonometry:
horizontal displacement = d * cos(40.0°)
Now we can calculate the work done by Bruno's force:
W2 = F2 * horizontal displacement
W2 = 11.0 N * (14.5 m * cos(40.0°))
Finally, we can find the net work done on the box by summing up the work done by Carol and Bruno:
Net work (W) = W1 + W2
Now you can substitute the values into the equations and calculate the net work done on the box.
To calculate the net work done on the box, you need to find the work done by each individual force and then add them together. Let's break it down step by step:
Step 1: Calculate the work done by Carol's force:
- Carol's force, Fc = 11.4 N
- Angle between Carol's force and displacement, θc = 40.0° downward from the horizontal
- Distance, d = 14.5 m
Using the formula W = Fd cosθ, where θ is the angle between the force and displacement:
Wc = 11.4 N * 14.5 m * cos(40.0°)
Step 2: Calculate the work done by Bruno's force:
- Bruno's force, Fb = 11.0 N
- Angle between Bruno's force and displacement, θb = 40.0° above the horizontal
- Distance, d = 14.5 m
Using the formula W = Fd cosθ, where θ is the angle between the force and displacement:
Wb = 11.0 N * 14.5 m * cos(40.0°)
Step 3: Calculate the net work done by adding the individual works together:
Net Work = Wc + Wb
Now you can calculate the net work done using these formulas. Make sure to use the correct values for the angles and calculate the cosine of the angles correctly.