Question

A 10-kg toy truck is pulling a 2-kg empty bucket on a frictionless incline. If the toy truck moves downward along the incline with an acceleration of 1.2 m/s?^2?. Given that the diameter of the pulley is 20-cm, and the incline angle is 45? degrees?. a) Find the mass of the pulley. b) Find the amount of water to add in the bucket so that the toy truck moves at constant speed downward.

Answer 1

here,

mass of toy car , m1 = 10 kg

mass of bucket , m2 = 2 kg

let the mass of pulley be m

a)

the accelration ,a = net force /effective mass

a = ( m1 * g * sin(theta) - m2 * g)/(m1 + m2 + 0.5 * m * R^2/R^2)

1.2 = ( 10 * 9.81 * sin(45) - 2 * 9.81 ) /(10 + 2 + 0.5 * m)

solving for m

m = 58.9 kg

the mass of pulley is 58.9 kg

b)

let the amount of water added be m3

for the accelration to be zero

the net force is zero

m1 * g * sin(theta) - (m2 + m3) * g = 0

10 * sin(45) = 2 + m3

m3 = 5.1 kg

the mass of water added is 5.1 kg