A 1200-kg car coasts from rest down a driveway that is inclined 20° to the horizontal and is 15 m long. How fast is the car going at the end of the driveway if (a) friction is negligible and (b) a friction force of 3000 N opposes the motion?
(a)
The speed of the car, of
Answer to Problem 46SP
Solution:
Explanation of Solution
Given data:
The mass of the car is
The angle of incline of the driveway with the horizontal is
The length of the driveway is
Formula used:
The expression for change in kinetic energy is written as
Here,
The expression for change in potential energy is written as
Here,
The expression for work energy theorem is written as
Explanation:
Draw the diagram for the motion of the car
There is no frictional force acting on the car, so there is no work done on the car. Therefore,
Substitute
The car started from rest. The initial velocity is zero. Also, the final position of the car is on the horizontal. Therefore,
Consider the diagram and the initial vertical distance covered is the sine component of the distance covered. Therefore,
Substitute
Conclusion:
The speed of the car at the end of the driveway with negligible frictional force is
(b)
The speed of the car, of
Answer to Problem 46SP
Solution:
Explanation of Solution
Given data:
The mass of the car is
The angle of incline is
The distance to the horizontal is
The frictional force is
Formula used:
The expression of change in kinetic energy is written as
Here,
The expression of change in potential energy is written as
Here,
The expression of frictional work done is written as
Here,
The expression for the work energy theorem is written as
Explanation:
Draw the diagram for the motion of the car
Recall that the expression for the work energy theorem is written as
Substitute
The car started from rest. The initial velocity is zero. Also, the final position of the car is on the horizontal. Therefore,
Consider the diagram and the initial vertical distance covered is the sine component of the distance covered. Therefore,
The frictional force acts in the opposite direction of the displacement. Therefore,
Substitute
Conclusion:
The speed of the car with a frictional force of
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Chapter 6 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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