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

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SUMMARY

The total work done on an object being dragged across a level floor and then up a ramp can be calculated using the formula W = F(d)Cosθ. In this case, a box is pulled 16 m on a flat surface with a force of 75N at an angle of 35 degrees, resulting in 982.98J of work. For the ramp portion, the angle between the force and the displacement must be determined, taking into account the ramp's 20-degree incline and the force's 35-degree angle to the floor. The solution simplifies to calculating the effective angle for the work done along the ramp.

PREREQUISITES
  • Understanding of work-energy principles in physics
  • Familiarity with trigonometric functions and angles
  • Knowledge of vector components of forces
  • Ability to apply the work formula W = F(d)Cosθ
NEXT STEPS
  • Calculate work done on an inclined plane using different angles
  • Explore vector decomposition of forces in physics
  • Learn about the effects of friction on work done
  • Study the relationship between force, displacement, and angle in various scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for practical examples of work done on inclined planes.

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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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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
 
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.
 

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