Question

7. A 0.31 kg cart on a horizontal frictionless track is attached to a string. The string! passes overadisk-shaped pulley of mass 0.08 kg and radius 0.012 mand moves without slipping. The string is pulled vertically downward with a constant force of 1.1 N. Find (a) the tension in the string between the pulley and the cart. [T = 1.261 (b) the acceleration of the cart. [o = 4.1 m/s]

anwsers are in brackets after the question

Answer 1

here,

the mass of cart , m1 = 0.31 kg

the mass of pulley , m2 = 0.08 kg

radius , r = 0.012 m

the applied force , F = 1.4 N

the acceleration of cart , a = net force /effective mass

a = F /(m1 + I2/r^2)

a = F /(m1 + 0.5 * m2 * r^2 /r^2)

a = ( 1.4 ) /(0.31 + 0.5 * 0.08)

a = 4.1 m/s^2

a)

the tension in the string between the pulley and the cart , T = m1 * a

T = 0.31 * 4.1 N = 1.26 N

b)

the acceleration of cart is 4.1 m/s^2