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**

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