Question

The driver of a 1450 kg car, initially traveling at 10.6 m/s, applies the brakes, bringing the car to rest in a distance of 24.0 m. Find the net work done on the car. Find the magnitude and direction of the force that does this work. (Assume this force is constant.)

A cyclist coasts up a 10.3° slope, traveling 19.0 m along the road to the top of the hill. If the cyclist's initial speed is 9.90 m/s, what is the final speed? Ignore friction and air resistance.

Find the minimum initial height h₁ of the roller coaster in the figure below if the roller coaster is to complete the loop, where h₂ = 24.6 m. Neglect friction.

Answer 1

b)

Angle of inclination θ = 10.3 degree

Distance covered S = 19 m

Initial speed u = 9.9 m/s

Acceleration a = - g sinθ = - 9.8*sin10.3 = -1.752 m/s²

From kinematic relation

Final velocity v = Sqrt[u² + 2aS]

                       = Sqrt[98.01 - 66.57 ]

                       = Sqrt[ 31.44 ]

                       = 5.607 m/s    

C)

The mass of the car is m

the initial height is h₁
Radius of the loop R = h₂ / 2 ==> h₂= 2R = 24.6m