Question

A 300-gram cart is on a frictionless horizontal track. A string attaches it to a hanging mass over a pulley at the end of the track. If the cart accelerates at a rate of 4 meters per second squared, how much mass is hanging off of the pulley? Please show work!

Answer 1

Mass of the cart, m1 = 300 g = 0.300 kg

Suppose the hanging mass = m2

acceleration of the mass m1, a = 4.0 m/s^2

Suppose T is the tension in the string.

For the cart the force-mass equation is -

T = m1*a = 0.300*4.0 = 1.20 N

For the hanging mass, force-mass equation is -

m2*g - T = m2*a

put the value of the variables -

m2*9.81 - 1.20 = m2*4.0

=> m2*(9.81 - 4.0) = 1.20

=> m2 = 1.20 / (9.81 - 4.0) = 0.2065 kg = 206.5 g

Hence the mass hanging off the pulley = 206.5 g (Answer)