Checking to see if I'm right or not.

[Pinkshell4u]

Checking to see if I'm right...or not.

Homework Statement

A hill is 100 m long and makes an angle of 12 degrees with the horizontal. As a 50-kg jogger runs up the hill, how much work does gravity do on the jogger?

Homework Equations

Do I use PEg=mgDelta Y ?

The Attempt at a Solution

PEg = (50 kg) (9.8 m/s2) (100m) which equals 49,000 which is wrong. I know the answer is -10,000 J.

How and why? So confused...

 

[fizzynoob]

work is

$$\int\vec{F}\bullet dr$$

to get rid of the dot product, you must take the parallel component of the distance that it is in the same direction of the force (gravity..which is down)

so you get :

-F*d*sin($$\theta$$) = -mg*d*sin($$\theta$$) = -(50)(9.8)*100*sin(12)

 

[Pinkshell4u]

Oh, I think I get it. Thanks alot.

 

[fizzynoob]

no problem, remember that when you have the expression for work as:

F * D

that D is the change in distance, so say you climb a mountain than you climb back down than the work overall is zero since the change in position is zero

 

[rwisz]

I would first like to commend you for attempting to solve this problem and seeking clarification when you encountered difficulties. This shows a great attitude towards learning and problem-solving.

To answer your question, yes, you are on the right track by using the equation PEg=mgΔy to calculate the work done by gravity. However, the negative sign in your final answer indicates that the work done by gravity is actually in the opposite direction of the jogger's motion. This is because gravity is acting downwards, while the jogger is moving upwards.

Another important factor to consider is the angle of the hill. In this case, the jogger is not moving directly upwards, but at an angle of 12 degrees. This means that the force of gravity is not acting directly against the jogger's motion, but at an angle. To account for this, we need to use the component of gravity that is acting in the direction of the jogger's motion, which is given by mgcosθ, where θ is the angle of the hill.

Therefore, the correct equation to use in this case is PEg=mgcosθΔy. Substituting the values, we get:

PEg=(50 kg)(9.8 m/s^2)(cos12)(100m)= -10,000 J

I hope this explanation helps to clarify your confusion. Remember, in physics, it is important to pay attention to the direction of forces and the effects of angles when solving problems. Keep up the good work!