1. A car is rolling down a ramp that is inclined at and angle of 6.5 degree with
ID: 3893664 • Letter: 1
Question
1. A car is rolling down a ramp that is inclined at and angle of 6.5 degree with respect to horizontal. There is no friction acting from the road on the tires.
Employ conservation of mechanical energy to find the speed of a car that starts from rest and rolls down the ramp a distance of 36 m.
2. A car is rolling down a ramp that is inclined at and angle of 9.2 degree with respect to horizontal. There is no friction acting from the road on the tires.
Employ Newton's Law to find the speed of a car that starts from rest and rolls down the ramp a distance of 49 m.
3.You drive your 1,338-kg car at a constant speed of 23 mph a distance of 65 m down a ramp that has a grade of 11 %. Use conservation of energy to find the work done by the frictional force acting from the road on the tires. Define positive direction in the forward direction.
Explanation / Answer
Ok for number 1:
You must find the height of the hill.
1) sin6.5=x/36.....this equals 4.08m
2)PE=MGH=9.81(M)(4.08)=39.98M
3)Set PE equal to KE....39.98M=(.5)(M)(V^2)
4)39.98=.5(V^2)
5)V^2=79.96
6)V=8.94m/s
For number 2
1)sin9.2=x/49=7.83
2)PE=M(9.81)(7.83)=76.85M
3)76.85M=(.5)(M)(V^2)
4)153.71=V^2
5)V=12.40m/s
For number 3
You must use similar triangles to find the starting height of the car for the assigned grade of the slope.
1) for and 11% grade you will have the height of a triangle be 11 and the base be 100...you now will use the pythagorean theorm to find the hypotenuse to be 100.60318
2)Set up a proportion with rise over run for the similar triangles...
3) 11/100.60318=X/65
4)By solving this for X you will find the starting height to be 7.11m....
5) Now use PE+KE+W=PE(final)+KE(Final)
6) 1338(9.81)(7.11)+(.5)(1338)(10.28)+W(65)=(.5)(1338)(10.28)
7) The KE cancels out and you are left with W=-1435.76J
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