A cylindrical pulley with a mass of 4.4 kg, radius of 0.816 m and moment of inertia 1 2 M r2 is used to lower a bucket with a mass of 3.1 kg into a well. The bucket starts from rest and falls for 2.9 s. r M m What is the linear acceleration of the falling bucket

5.85 m/s²

Explanation:

Mass of pulley (M) = 6.8 kg, mass of bucket (m) = 1.5 kg, radius of pulley (r) = 0.816 m, acceleration due to gravity (g) = 10 m/s².

Let the tension exerted on the pulley be T and the angular acceleration be α,

The angular acceleration (α) = a / r; where a is the linear acceleration.

mg - T = ma

T = m(g - a)

Also, for the disk:

Tr = Iα

I = moment of inertia = 0.5Mr²

m(g - a)r = 0.5Mr²(a/r)

m(g - a)r = 0.5Mra

2m(g - a) = Ma

2mg - 2ma = Ma

Ma + 2ma = 2mg

a(M + 2m) = 2mg

a = 2mg / (M + 2m)

Substituting:

a = 2(3.1 kg)(10 m/s²) / (4.4 + 2(3.1))

a = 5.85 m/s²

the force on the thing and the distance the force moves the thing

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