Answer to Question #243249 in Physics for megs

Question

A dynamics cart with a mass of 3.7 kg is connected via a string across a pulley to an object with a mass of 1.3 kg. The cart is placed on a table while the mass hangs freely under the effect of gravity. Due to the smooth wheels of the cart, the effect of friction for this problem can be disregarded. Determine the tension in the string.

Answer 1

Write equations for forces according to Newton's second law for the cart of mass M and the hanging mass m. Assume that positive x is to the right, positive y is upward.

$$Ma=T,\\ -ma=-mg+T.\\\space\\ a=\frac TM,\\\space\\ -T\frac{m}{M}=-mg+T,\\\space\\ T=g\frac{Mm}{M+m}=9.43\text{ N}.$$