Question

We can use the range equation to calculate the horizontal range of any projectile. True or false

A small cart of mass m = 0.139 kg is moving at a constant speed v = 3.35 m/s on the inside of a vertical circular track with radius 4.74. Calculate the normal force (in Newtons) that the track exerts on the cart at its topmost point.

Answer 1

True , We can use the range equation to calculate the horizontal range of any projectile , which is derived from the equations of motions along horizontal distance considering only the vertical velocity will change.

Given
mass of small cart m = 0.139 kg
moving with constant speed v = 3.35 m/s ,inside the vertical circle of radius r = 4.74 m

as the cart is moving with constant force then the forces at the top of the circle are

the force of gravity(weight) acts downwards and the normal force on the cart by the tract at the top is also downward, that is

   F_N+mg = m*a
   F_N+mg = m*v^2/r

   F_N = m*v^2/r - m*g
   F_N = m(v^2/r - g )

substituting the values

   F_N = 0.139(3.35^2/4.74 - 9.8) N

   F_N = -1.033 N