a car is circling counter clockwise and is halfway up a loop, label on the figur

Question

a car is circling counter clockwise and is halfway up a loop, label on the figure itself the cars velocity, its acceleration vector due to its decreasing speed, and its acceleration vector due to its changing direction. A 4.0 kg ball is inside the car. It experiences two normal forces from the bottom and back of the seat. The roller coaster has a velocity of 24 m/s, acceleration of 6.95 m/s2 and the circles radius is 17 meters, find the value for the two normal forces. Ignore friction. What is the magnitude and direction of the total force exerted by the ball onto the seat? Both normal forces can be thought of as the components of the total normal force that the seat exerts on the ball.

Explanation / Answer

m = 4.0 kg, v = 24 m/s, at = 6.95 m/s^2, r = 17 m, an = v^2/r = 33.88 m/s^2 Ft = m*at = 27.8 N (along tangent) Fn = m*an = 136 N (towards the center) total force = 139 N angle with radius = arctan(Ft/Fn) = 11.6 degrees

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