PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A 5.0kg motorized cart travels along a straight, horizontal track. The cart’s motor provides a constant forward thrust force of 40N. While the cart moves, it experiences two retarding forces: (1) kinetic friction with coefficient 0.05 between the cart’s wheels and the track, and (2) an air-drag force whose magnitude is given by Fd=0.10v, where v is the cart’s speed in m/s.
(a) Write an expression for the magnitude of the normal force acting on the cart.
(b) Obtain an expression for the net horizontal force on the cart as a function of its speed v.
(c) Derive an expression for the cart’s acceleration a(v) as a function of speed.
(d) Determine the cart’s speed when its acceleration equals one-half of its initial acceleration (the acceleration at v=0).
(e) Calculate the terminal speed the cart approaches after a long time.