1. A 2,022-kg car is moving up a road with a slope (grade) of 20% while speeding

Question

1. A 2,022-kg car is moving up a road with a slope (grade) of 20% while speeding up at a rate of 2.1 m/s^2. What is the direction and magnitude of the frictional force? (define positive in the forward direction, i.e., up the slope)?

2. A 1,953-kg car is moving up a road with a slope (grade) of 13% while slowing down at a rate of 4.4 m/s^2. What is the direction and magnitude of the frictional force?

(define positive in the forward direction, i.e., up the slope)?

3. A 1,832-kg car is moving up a road with a slope (grade) of 23% while slowing down at a rate of 1.7 m/s^2. What is the direction and magnitude of the frictional force?
(define positive in the forward direction, i.e., up the slope)?

Explanation / Answer

net force Ma = W-f

also Use V = u-at   ( acs csar decelerates)

so Ma = W-f   = Mg sin theta - F cos theta

F   = M(g sin theta -a)/cos theta is the formua in all cases

so here apply

a. theta = 20 radians

so F = 2022*(9.8 sin (20 rads) -2.1)/cos (20 rad)

F = +33925.42 N

w and f are forces directed along the surface of the road
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b. F = 1953 * ( 9.8 *sin (13 rad)-4.4)/cos (13 rad)

F = -607.699 N

w and f are forces directed along the surface of the road
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F = 1832 * (9.8 sin (23) -1.7)/cos (23 rad)

F = + 34358.04 N

w and f are forces directed along the surface of the road
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