Angela is riding in a sled sliding along (nearly) frictionless ice at 3.5 m/s. H
ID: 1883137 • Letter: A
Question
Angela is riding in a sled sliding along (nearly) frictionless ice at 3.5 m/s. Her and the sled have a combined mass of 55 kg. She then leaves the ice and enters a long patch of snow which has coefficients of friction µs = 0.15 and µk = 0.050 with the sled.
a. How far does she slide on the snow before coming to rest?
b. Assume that Angela got to her initial speed by going down a snowy hill at an angle of 20°to the ground, and that this snow has the same coeffients of friction as above. How tall is the hill?
Explanation / Answer
a)
Using workenergy theorem
Workdone by friction = change in kinetic energy of sled and body
(uk) mgd= 0.5mv^2
0.05* 9.8*d= 0.5* 3.5^2
d= 12.5 m
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net acceleration of the object along downwards
a= g sin x - (uk) g cos x
= 9.8( sin 20- 0.05* cos 20)
= 2.89 m/s^2
using 3rd equation of motion
D= v^2/(2a)= 3.5^2/(2* 2.89 )
D= 2.12 m
Vertical height of hill= D sin 20= 0.725 m
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Commemt in case any doubt.. good luck