Find the total work done on an object on a ramp if the force is at an angle?

In summary, the problem involves a box being dragged by a force of 75N at an angle of 35 degrees to the floor. The box is then dragged up a ramp inclined at 20 degrees to the floor. The total work done by the force is calculated by using the equation W= F(d)Cosθ, where θ is the angle between the force and displacement. In the first part, the work is calculated to be 982.98J. In the second part, the angle between the force and the ramp is found to be 15 degrees, and the work done is calculated using the same equation.
  • #1
misplaced1
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Homework Statement


A box is dragged 16 m across a level floor by a 75N force at an angle of 35 degrees to the floor . It is then dragged by the same force 8m up a ramp inclined at an angle of 20 degrees to the floor. Determine the total work done by the force.

Homework Equations



W= F(d)Cosθ

The Attempt at a Solution



Part 1

W= (75)(16)Cos(35)
W= 982.98J

Part 2

I am not sure how to do this part, because θ is defined as being the angle between the force and the displacement. Where does the ramp fit in? Should I take the force of gravity perpendicular to the ramp (the normal force) and add that to the vertical component of my applied force?
 
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  • #2
Find the angle between the applied force and displacement along the ramp. The ramp is inclined at 20 degrees to the floor, the force is at 35 degrees to the floor, what is the angle between the force and ramp?

ehild
 
  • #3
Thank you for your help. I think that I was over-thinking the question. It really is so much simpler than I was making it out to be.
 

Related to Find the total work done on an object on a ramp if the force is at an angle?

What is the formula for finding the total work done on an object on a ramp?

The formula for finding the total work done on an object on a ramp is W = Fd cosθ, where W is the work done, F is the applied force, d is the displacement, and θ is the angle between the force and the displacement.

How do you calculate the angle between the force and the displacement?

To calculate the angle between the force and the displacement, you can use the dot product formula: θ = cos^-1(F · d / |F||d|), where F · d is the dot product of the force and displacement vectors, and |F| and |d| are the magnitudes of the vectors.

What is the unit of measurement for work?

The unit of measurement for work is joules (J), which is equivalent to kg·m^2/s^2 in the SI system.

Can the work done on an object on a ramp be negative?

Yes, the work done on an object on a ramp can be negative if the applied force is in the opposite direction of the displacement. This indicates that the object is losing energy as it moves down the ramp.

How does the angle affect the total work done on an object on a ramp?

The angle between the force and displacement affects the total work done on an object on a ramp by changing the effective force acting on the object. The greater the angle, the less of the force is acting in the direction of motion, resulting in less work being done.

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