(b)What is the maximum speed the car can have without losing contact with the gr
ID: 1691873 • Letter: #
Question
(b)What is the maximum speed the car can have without losing contact with the ground as it passes the highest point? I have set up force diagrams for the car and am having trouble because there isnt a force in the x-direction. It is confusing me. Help please.A car of mass m passes over a hump in a road that follows the arc of a circle of radius R as shown in the figure. (a) If the car travels at a speed v, what force does the road exert on the car as the car passes the highest point of the hump? (Use any variable or symbol stated above along with the following as necessary: g.) (b)What is the maximum speed the car can have without losing contact with the ground as it passes the highest point? I have set up force diagrams for the car and am having trouble because there isnt a force in the x-direction
Explanation / Answer
Correct, there is no force in the x-direction, but we don't need it. We want to find F(normal), which points upward. F(gravity) points downward, as does F(centripetal). F(centripetal) is not a "real" force, but rather the resultant force calculated by adding the vectors of all other forces: F(centripetal) = F(gravity) - F(normal) Now solve for F(normal): F(normal) = F(gravity) - F(centripetal) = mg - (mv^2)/R The maximum speed the car may have occurs when F(normal) = 0. Any faster and it will fly off the track (since normal force cannot go negative and change direction to hold it on the road.) 0 = mg - (mv^2)/R; (mv^2)/R = mg; v^2 = mgR/m; v = sqrt(gR)
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