(a) For the car going up the incline, what percentage of the work done by the suspended weight was lost to friction? (b) For the car moving down the incline, what percentage of the work done by gravity was lost to friction? (Show your calculations.)
(a)
The percentage of work done by the suspended weight that is lost to friction when a car is moving up an incline with constant speed.
Answer to Problem 3Q
The percentage loss of energy by the suspended weight is
Explanation of Solution
Draw a diagram to show the different components of forces acting on the car.
Write the expression for the net horizontal force acting on the car
Here,
Write the expression for the force acted upon the car by the pull of the mass
Here,
Write the expression for the work done by the frictional force.
Here,
Write the expression for the percentage loss of energy.
Here,
Write the expression for the work done by the suspended weight.
Here,
Conclusion:
Substitute
Substitute
Substitute
For
Substitute
Substitute
Divide expression (VII) by (VI).
Here,
Substitute
For
Substitute
Substitute
Divide expression (IX) by (VIII).
Here,
Substitute
Thus, the percentage loss of energy by the suspended weight is
(b)
The percentage of work done by gravity that is lost to friction when a car is moving down an incline with constant speed.
Answer to Problem 3Q
The percentage loss of energy by gravity is
Explanation of Solution
Draw a diagram to show the different components of forces acting on the car.
Write the expression for the net horizontal force acting on the car
Here,
Write the expression for the force acted upon the car by the pull of the mass
Here,
Write the expression for the work done by the frictional force.
Here,
Write the expression for the percentage loss of energy.
Here,
Write the expression for the work done by the suspended weight.
Here,
Conclusion:
Substitute
Substitute
Substitute
For
Substitute
Here,
Substitute
Divide expression (XVII) by (XVI).
Here,
Substitute
Here,
For
Substitute
Here,
Substitute
Divide expression (XIX) by (XVIII).
Here,
Substitute
Here,
Thus, the percentage loss of energy by gravity is
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Chapter 12 Solutions
Physics Laboratory Experiments
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