How would you find force in this problem?

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To determine the force exerted by the worker loading the refrigerator, the angle of the ramp is crucial. The ramp creates a right triangle, but the force should be considered parallel to the slope, making the angle between force and displacement zero. The formula for work, W = Fd(cosθ), indicates that if the force is parallel to the displacement, the angle θ should not be included. The correct calculation shows that the force required is 360 N, not the previously calculated 376.4 N. Understanding when to apply angles in work calculations is essential for accurate results.
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A worker uses a ramp to slide a refrigerator onto the back of the truck. The ramp is 5.0m long, and raises the refrigerator 1.5m above the ground. The amount of work done by the worker is 1800J. What is the magnitude of the force the worker must exert to load the refrigerator?

Ok so the first thing I did was calculate the angle by doing tangent^-1 (1.5/5.0) and got 17 degrees. Then I multiplied cos(17) and and 5.0 and divided it by 1800.
When I looked on the answer sheet it said the force was 3.6X10^2. I got 376.4. What did I do wrong?! I figured you calculate the angle since he is pushing the fridge at that degree up the ramp. Isn't the formula W=Fd(cosθ)? The answer sheet said I shouldn't have the degree, why?
 
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tangent is opposite over adjacent, not opposite over hypotenuse (that's sine)

the ramp is forming the hypotenuse of the right triangle
 
ok, but shouldn't it have some sort of angle since the worker is pushing it up. I used tangent to find the angle.
 
Merlan114 said:
Ok so the first thing I did was calculate the angle by doing tangent^-1 (1.5/5.0) and got 17 degrees. Then I multiplied cos(17) and and 5.0 and divided it by 1800.
When I looked on the answer sheet it said the force was 3.6X10^2. I got 376.4. What did I do wrong?! I figured you calculate the angle since he is pushing the fridge at that degree up the ramp. Isn't the formula W=Fd(cosθ)? The answer sheet said I shouldn't have the degree, why?

5cos(17) is the horizontal component of the displacement which is along the slope at angle 17° with respect to the horizontal. If you divide it by 1800 you can not get a 376.

The worker pushes the block along the slope. He needs the smallest force if the force is parallel with the slope. The displacement is 5 m along the slope. If the force and displacement are parallel, theta is zero.

ehild
 
So when do I know to use an angle?
 
Merlan114 said:
So when do I know to use an angle?

When you calculate work you need to use the angle between displacement and force. In this case, the angle is zero.

ehild
 

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