Answer to Question #263204 in Physics for Nick

Question

A force of 20N pulls two carts tied together with a string. The carts with masses 3kg and 4kg, respectively, run on a smooth level surface. Find :

a. The acceleration of the 4kg cart

b. The acceleration of the 3kg cart

c. The tension on the string connecting the two carts.

Answer 1

(a)-(b)

$$a_1=a_2=a,$$ $$F=(m_1+m_2)a,$$ $$a=\dfrac{F}{(m_1+m_2)}=\dfrac{20\ N}{(3\ kg+4\ kg)}=2.86\ \dfrac{m}{s^2}.$$

(c)

$$F-T=m_1a,$$ $$T=F-m_1a=20\ N-3\ kg\times2.86\ \dfrac{m}{s^2}=11.42\ N.$$