**You are required to write out the math steps for every derivation asked for; if you do not then you will not get credit for your answer. Put boxes around your final answers.**

- A person applies a pull force F
_{pull}of 100N to a 20 kg box to to pull it down a 30^{o}ramp; he applies the pull force at 30^{o}counterclockwise from the ramp incline. Another person applies a push force F_{push}of 50N to the box (and parallel to the ramp) to help push it down the ramp (see figure). The coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.25

a) Using Newton’s 2^{nd} Law derive the formula for the Normal force function, and then calculate the normal force value:

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Write My Essay For Meb) Using Newton’s 2^{nd} Law derive the acceleration **function** in terms of angles, mass, & *g, *and then solve for the acceleration value:

c) Calculate after 5 seconds how far has the sled has moved

2) A 4 kg rock tied to the end of a 3m long string is swung in a circle at constant speed of 100 feet/sec; (ignore gravity). After it’s swung around for 20 seconds derive the following quantities:

a) Centripetal acceleration:

b) Total acceleration:

c) Centripetal force:

d) The number of revolutions the rock went through:

e) The period and frequency

f) Draw the rock in its circular motion with all the vectors to scale in parts a) b) and c)

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