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(practice exam question) The work energy theorem states that the work done by al

ID: 2025261 • Letter: #

Question

(practice exam question)

The work energy theorem states that the work done by all the forces acting on an object is equal to the change in its kinetic energy. Use the concepts of work and energy to answer the following. (Note, this question can also be answered using Newton's laws and calculating accelerations. NO MARKS will be awarded for answering the question this way. Be sure to explain your logic and any assumptions you have made when answering the questions). Starting from rest, a 80.0 kg skier slides down a frictionless snow-covered slope, along a short horizontal section, over a small jump and into the air, see below. The slope of the jump is 30 degree to the horizontal. How fast is the skier moving when they are on the short horizontal section? What is the maximum height (above the level of the short horizontal section) that the skier reaches after leaving the jump? If the skier makes a smooth frictionless landing after the jump, then what will their speed be then?

Explanation / Answer

Eo = Ef
Ko + Uo = Kf + Uf
.5mvo2 + mgho = .5mvf2 + mghf 
.5(80)(02) + 80(9.81)(35) = .5(80)(v2) + 80(9.81)0
27468 = 40v2 
v2 =  686.7
v = 26.20 m/s 

breaking v into x, y components @ ramp
v = 26.2cos30 i + 26.2sin30 j
v = 22.69 i + 13.1 j

v2 = vo2 + 2ay 
0 = 26.22 + 2(-9.81)y
-686.7 = -19.62y
y = 35 meters

 

The speed would be the same according to the theorem since he would be landing at the same change in height.