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An automobile drives over some hilly terrain. The motion of the automobile at the top of a hill is instantaneously similar to circular motion with the center of curvature beneath the road. The motion of the automobile at the bottom of a dip is instantaneously similar to circular motion with the center of curvature above the road. At any time there are three forces on the car: weight , normal , and friction of the tires with the road. The magnitudes of these three forces are given respectively by W, N, and f. (a) When the car is at the top of a hill, which of the following gives the magnitude of the centripetal force? (A) N (B) W + N (C) W - N (D) N - W (b) When the car is at the bottom of a dip, which of the following gives the magnitude of the centripetal force? (A) N (B) W + N (C) W - N (D) N – W

An automobile drives over some hilly terrain. The motion of the automobile at the top of a hill is instantaneously similar to circular motion with the center of curvature beneath the road. The motion of the automobile at the bottom of a dip is instantaneously similar to circular motion with the center of curvature above the road. At any time there are three forces on the car: weight , normal  , and friction of the tires with the road. The magnitudes of these three forces are given respectively by W, N, and f.
(a) When the car is at the top of a hill, which of the following gives the magnitude of the centripetal force?
(A) N                                    (B) W + N 
(C) W - N                              (D) N - W
(b) When the car is at the bottom of a dip, which of the following gives the magnitude of the centripetal force?
(A) N                                    (B) W + N 
(C) W - N                             (D) N – W

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
(a)
The correct option is:
(C) W – N.
(b)
The correct option is:
(D) N – W.
(a)
The figure below shows the normal force \overrightarrow{N}and the weight \overrightarrow{W}acting on the automobile on the top of a hill, and is equivalent to circular motion with the center of curvature beneath the road:
233-185_23.PNG
It can be seen from the figure above that both the vectors \overrightarrow{N}and \overrightarrow{W}point in the opposite direction, and contributes to the centripetal force. Therefore, the magnitude of centripetal force is Fc = W – N.
Thus, (C) is the correct option, while the rest are ruled out.
(b)
The figure below shows the normal force \overrightarrow{N}and the weight \overrightarrow{W}acting on the automobile on the bottom of a hill, and is equivalent to circular motion with the center of curvature above the road:
233-1399_24.PNG
It can be seen from the figure above that both the vectors \overrightarrow{N}and \overrightarrow{W}point in the opposite direction, and contributes to the centripetal force. Therefore, the magnitude of centripetal force is Fc = N – W.
Thus, (D) is the correct option, while the rest are ruled out.

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