Problem 4 A block is attached to a disk-shaped pulley (see picture below) The ma

Question

Problem 4 A block is attached to a disk-shaped pulley (see picture below) The mass of the pulley is mp = 0.8 kg and its radius is R = 0.4 m. The mass of the block is m = 1.3 kg. (a) Find the acceleration of the block. (b) what is the tension in the string as the block is accelerating? (c) If the block is released from rest, at a height 0.6 m above the ground, how long does it take for it to strike the ground? Rod about Solid cylinder or disc, symmetry axis symmetry axis Solid sphere Hoop about 2 12 12 Solid cylinder ntral diameter Hoop about diameter Thin spherical shell Rod about

Explanation / Answer

for

block

along vertical

net force Fy = m*a

mg - T = m*a

T = mg - ma ..........(1)

for the pulley

net torque acting = I*alpha

I = moment of inertia = (1/2)*M*R^2

alpha = angular acceleration = a/R

a = accelration

net torque = T*R

therefore

T*R = (1/2)*mp*R^2*a/R

T = (1/2)*mp*a........(2)

substituting 1 in 2

mg - ma = (1/2)*mp*a

a = mg/(m + mp/2)

acceleration a = 1.3*9.8/(1.3 + 0.8/2) = 7.5 m/s^2 <<<-------ANSWER

======================================

part (b)

from 2

T = mp*a/2 = 0.8*7.5/2 = 3 N <<<<--------ANSWER

======================

part(c)

along vertical

initial velocity voy = 0

acceleration ay = -7.5 m/s^2

displacement y = -h = -0.6 m

y = voy*t + (1/2)*ay*t^2

-0.6 = 0 - (1/2)*7.5*t^2

time taken t = 0.4 seconds <<<<---------ANSWER

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