Question

A block (mass = 1.7 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.0 x 10-3 kg·m2), as the figure 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 0.045 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord.

Answer #1

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A block (mass = 2.3 kg) is hanging from a massless cord that is
wrapped around a pulley (moment of inertia = 1.7 x 10-3 kg·m2), as
the figure 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...

A block (mass = 1.2 kg) is hanging from a massless cord that is
wrapped around a pulley (moment of inertia = 1.0 x 10-3 kg·m2), as
the figure 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...

A block (mass = 1.0 kg) is hanging from a massless cord that is
wrapped around a pulley (moment of inertia = 1.1 x 10-3
kg·m2), as the figure 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...

A block (mass = 3.0 kg) is hanging from a massless cord that is
wrapped around a pulley (moment of inertia = 1.2 x 10-3 kg·m2), as
the figure 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...

A block (mass = 2.4 kg) is hanging from a massless cord that is
wrapped around a pulley (moment of inertia = 1.8 x 10-3 kg·m2), as
the figure 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...

A block (mass = 59.1 kg) is hanging from a massless cord that is
wrapped around a pulley (moment of inertia = 1/2MR2 kg ·
m2, where M = 6.9 kg is the mass of the pulley and R=1.3
m is its radius ), 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...

A hanging weight, with a mass of m1 = 0.365
kg, is attached by a cord to a block with mass
m2 = 0.815 kg as shown in the figure below. The
cord goes over a pulley with a mass of M = 0.350 kg. The
pulley can be modeled as a hollow cylinder with an inner radius of
R1 = 0.0200 m, and an outer radius of
R2 = 0.0300 m; the mass of the spokes is
negligible. As...

To start her lawn mower, Julie pulls on a cord that is wrapped
around a pulley. The pulley has a moment of inertia about its
central axis of III = 0.590 kg⋅m2kg⋅m2 and a radius of 4.00 cmcm .
There is an equivalent frictional torque impeding her pull of
τfτftau_f = 0.260 m⋅Nm⋅N .
To accelerate the pulley at ααalpha = 4.35 rad/s2rad/s2 , how
much torque does Julie need to apply to the pulley?
How much tension must the...

4. A massless rope is wrapped around a uniform solid
cylinder that has radius of 30 cm and mass 10 kg, as
shown in the figure. The cylinder begins to unwind when it is
released and allowed to rotate.
(a) What is the acceleration of the center of mass of the
cylinder?
(b) If 90 cm of rope is unwound from the cylinder as it falls, how
fast is it rotating at this instant?

A hanging object has a mass of m1 = 0.435 kg; the sliding block
has a mass of m2 = 0.880 kg; and the pulley is a hollow cylinder
with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and
an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is
negligible. The coefficient of kinetic friction between the block
and the horizontal surface is ?k = 0.250....

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