How can I calculate the work needed to pull a toboggan up an inclined hill?

In summary, the problem involves a child pulling a toboggan up a hill with a given mass and angle of inclination. The task is to calculate the work done by the child to pull the toboggan at a constant velocity. The correct equation to use is W=FD cos(angle), but the mistake in the solution was using the wrong value for D. The correct answer is 1.29 x 10^3 J.
  • #1
ka7
3
0
[SOLVED] Work and energy

Hello, I've been having difficulty with this question...

Homework Statement



A 25.6kg child pulls a 4.81kg toboggan up a hill inclined at 25.7° to the horizontal. The vertical height of the hill is 27.3 m. Friction is negligible. Determine how much work the child must do on the toboggan to pull it at a constant velocity up the hill.



Homework Equations



W=FD COS (ANGLE)

The Attempt at a Solution



I tried using the equation above...and i tried adding the masses ...I got the wrong answer. The force, I used F=mg
w=mgd cos (angle)
=(4.81) (9.8) (27.3) cos (25.7)
=1.15 x 10^3 J
the answer 1.29 x 10^3 J but I'm not geting that...:confused:
 
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  • #2
Welcome to the forums ka7,

HINT: What is the change in gravitational potential energy of the toboggan? (Much easier :wink:)
 
  • #3
You should recheck what the D in your formula means. It is presumably NOT the vertical height of the hill.
 
  • #4
Thanks, i figured out what i was doing wrong:smile:
 

Related to How can I calculate the work needed to pull a toboggan up an inclined hill?

1. What is the definition of work and energy difficulty?

The concept of work refers to the transfer of energy that occurs when a force is applied to an object and the object is displaced in the direction of the force. Energy difficulty, on the other hand, is a subjective measure of how much effort or difficulty is required to complete a task or accomplish a goal.

2. How are work and energy difficulty related?

The amount of work done on an object is directly related to the amount of energy needed to overcome the resistance or difficulty of the task. In other words, the more work that is required, the more energy is needed to accomplish it.

3. What factors affect work and energy difficulty?

The amount of work and energy difficulty can be affected by various factors, such as the force applied, the distance the object is displaced, and the direction of the force relative to the displacement. Other factors may include the weight or mass of the object, friction, and the type of surface the object is moving on.

4. How can we measure work and energy difficulty?

Work and energy difficulty can be measured using various methods, such as calculating the amount of force applied and the distance the object is displaced. Additionally, subjective measures such as self-report surveys or task completion time can also be used to assess the perceived difficulty of a task.

5. What are some real-world applications of work and energy difficulty?

Understanding work and energy difficulty is essential in various fields, including physics, engineering, and sports. In physics, it helps explain the motion of objects and the transfer of energy. In engineering, it is crucial for designing efficient machines and structures. In sports, it is used to optimize training and performance by understanding how much energy is needed to complete certain tasks or exercises.

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