Construction Site: At a construction site, a 65.0 kg bucket of concrete hangs fr

Question

Construction Site: At a construction site, a 65.0 kg bucket of concrete hangs from a light (but strong) cable that passes over a light, friction-free pulley and is connected to an 80.0 kg box on a horizontal roof (see figure). The cable pulls horizontally on the box, and a 50.0 kg bag of gravel rests on top of the box. The coefficients of friction between the box and roof are shown. (a) Find the friction force on the bag of gravel and on the box. (b) Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended 2.00 m from rest. (Use Newton's laws to check your answer.) [LO 27, LO 28 or 29, LO 32, LO 34, LO 36, LO 37, LO 38, LO 39] . Gravel Box 0.700 0.400 Concrete

Explanation / Answer

here,

mass of bucket , m1 = 65 kg

mass of box , m2 = 80 kg

mass of bag , m3 = 50 kg

a)

as the system will not move

the frictional force acting on bag of gravel and box , ff = net force applied

ff = m1 * g

ff = 65 * 9.81 = 637.7 N

b)

when the bag is removed

the accelration , a = net force /effective mass

a = ( m1 * g - uk * m2 * g)/(m1 + m2)

a = ( 65 * 9.81 - 0.4 * 80 * 9.81) /( 80 + 65) m/s^2

a = 3.04 m/s^2

the speed of bucket at s = 2 m , v = sqrt(2 * a * s)

v = sqrt(2 * 3.04 * 2) m/s

v = 3.5 m/s

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