Concept explainers
A car with a mass of 1100 kg is traveling around a curve with a radius of 50 m at a constant speed of 25 m/s (56 MPH). The curve is banked at an angle of 12 degrees.
- a. What is the magnitude of the centripetal acceleration of the car?
- b. What is the magnitude of the
centripetal force required to produce this acceleration? - c. What is the magnitude of the vertical component of the normal force acting upon the car to counter the weight of the car?
- d. Draw a diagram of the car (as in fig. 5.8) on the banked curve. Draw to scale the vertical component of the normal force. Using this diagram, find the magnitude of the total normal force, which is perpendicular to the surface of the road.
- e. Using your diagram, estimate the magnitude of the horizontal component of the normal force. Is this component sufficient to provide the centripetal force?
(a)
The magnitude of the centripetal acceleration of the car.
Answer to Problem 3SP
The magnitude of the centripetal acceleration of the car is
Explanation of Solution
Given Info: The radius of the curve is and the speed of the car is
Write the equation for the centripetal acceleration.
Here,
Substitute
Conclusion:
Thus the magnitude of the centripetal acceleration of the car is
(b)
The magnitude of the centripetal force required to produce the centripetal acceleration.
Answer to Problem 3SP
The magnitude of the centripetal force required to produce the centripetal acceleration is
Explanation of Solution
Given Info: The mass of the car is
Write the equation for centripetal force.
Here,
Substitute
Conclusion:
Thus the magnitude of the centripetal force required to produce the centripetal acceleration is
(c)
The magnitude of the vertical component of the normal force acting upon the car to counter the weight of the car.
Answer to Problem 3SP
The magnitude of the vertical component of the normal force acting upon the car to counter the weight of the car is
Explanation of Solution
Given Info: The mass of the car is
The vertical component of the normal force acts to counter the weight of the car so that vertical component of normal force is equal to the weight of the car.
Write the equation for the weight of the car.
Here,
The value of
Substitute
Conclusion:
Thus the magnitude of the vertical component of the normal force acting upon the car to counter the weight of the car is
(d)
Diagram of the car on the banked curve to scale the vertical component of the normal force and determine the magnitude of the total normal force.
Answer to Problem 3SP
The diagram of the car on the banked curve is
and the magnitude of the total normal force is
Explanation of Solution
Given Info: The angle of banking of the curve is
The diagram of the car in the curve is shown in figure 1.
Figure 1
Write the equation for the vertical component of the normal force.
Here,
Rewrite the above equation for
Substitute
Conclusion:
Thus the diagram of the car on the curve is drawn in figure 1 and the magnitude of the total normal force is
(e)
The magnitude of the horizontal component of the normal force and whether it is sufficient to provide the centripetal force.
Answer to Problem 3SP
The magnitude of the horizontal component of the normal force is
Explanation of Solution
Given Info: The angle of banking of the curve is
Write the equation for the horizontal component of the normal force.
Here,
Substitute
Conclusion:
Thus the magnitude of the horizontal component of the normal force is
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Chapter 5 Solutions
Physics of Everyday Phenomena
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