Question

A 28.0 kg block is connected to an empty 1.80 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.41 and the coefficient of kinetic friction between the table and the block is 0.31. Sand is gradually added to the bucket until the system just begins to move Calculate the mass of sand added to the bucket. Express your answer using two significant figures. Calculate the acceleration of the system. Express your answer using two significant figures.

Answer 1

here,

mass of the block , m = 28 kg

mass of the bucket , mb = 1.8 kg

let the mass of sand be ms

coefficient of static friction , us = 0.41

coefficient of kinetic friction , uk = 0.31

(a)

for the block just to move

( mb + ms) *g - us*m *g = 0

( ms + 1.8) *9.8 = 0.41*28* 9.8

ms = 9.78 kg

the mass of sand added is 9.78 kg

(b)

the accelration of system , a = ( ( ms + mb)*g - uk * m*g) /( m + mb + ms)

a = ( ( 9.78 + 1.8 ) *9.8 - 0.31*28 * 9.8) /( 28 + 9.78 + 1.8)

a = 0.72 m/s^2

the accelration of the system is 0.72 m/s^2