A block (mass = 2.2 kg) is hanging from a massless cord that is wrapped around a

Question

A block (mass = 2.2 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.5 10-3 kg · m2), as the drawing shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.043 m during the block's descent. Find the angular acceleration of the pulley and the tension in the cord.

Explanation / Answer

Let T be the string tension

then we have

Net force acting on block .. Fn = mg - T and also Fn = ma
T = m(g - a)
a = r
So .. T = m(g - r) ----- (1)

For the pulley .. Torque (T x r) = I. .. (I = mom of inertia)
T = I/r ----- (2)

On Combining 1 and 2

I/r = m(g - r)
I = mgr - mr²
= mgr / (I + mr²)

= (2.20 x 9.80 x 0.043) / (1.50^-3 + [2.20 x 0.043²])

= 166.5rad/s²

Plug = 166.5 rad/s² into Eq (1)
T = m(g - r)
T = 2.20(9.80 - [0.043 x 166.5])

T = 5.80 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.