Reviewing for my exam (Newton question)

[Chandasouk]

Homework Statement

You push a 20 kg box from an elevation of zero up a hill. You exert a force of 200 N for 6 m and the box speeds up steadily from rest to 2 m/s. There is a 100 N frictional force that opposes the box’s motion.

A) Draw energy bar charts to describe this motion. Be sure to describe your system, and the initial and final states.

B) At what elevation is the box moving when its speed is 2 m/s?

C) What angle does the hill make with the horizontal?






A) Initial (Bottom) Work = Final (Top) PE + KE+ $$\Delta$$U_internal

B) Givens

m=20kg
F-applied = 200N
F-friction = 100N
V = 2m/s
L(distance traveled) = 6m

H= ?

Fd = mgh + .5mv² + $$\Delta$$U_internal

(200N)(6m) = (20kg)(9.80m/s^2)h + .5(20kg)(2m/s)^2 + (100N)(6m)

1200J = 196h + 40J + 600J

600J = 196h + 40J

560J = 196h

H = 2.86m


C) tan$$\theta$$ = 2.86/6 = 25.5 degrees

Not sure if anything is correct to be honest.

 

[diazona]

Actually I think that's about right. Just make sure you're using the right trigonometric function for the last step.