d. Determine a symbolic expression for the acceleration of m2. Show that your result has units of acceleration. e. Suppose the pulley has radius R = 6.0 cm, mass M = 2.0 kg, the friction on the axle exerts a of magnitude T = 0.50 Nm, m, = 2.0 kg, m2 = 4.0 kg and d = 1.0 m. If the blocks are torque released from rest, how long does it take m2 to reach the floor? Show that your result has units of time.
d. Determine a symbolic expression for the acceleration of m2. Show that your result has units of acceleration. e. Suppose the pulley has radius R = 6.0 cm, mass M = 2.0 kg, the friction on the axle exerts a of magnitude T = 0.50 Nm, m, = 2.0 kg, m2 = 4.0 kg and d = 1.0 m. If the blocks are torque released from rest, how long does it take m2 to reach the floor? Show that your result has units of time.
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Just need help with part D and E. Please show steps.
Transcribed Image Text:1. We return to the Atwood machine from last term - a machine consisting of a pulley, a string, and
a system of masses. We will continue to assume a massless string, but we will relax the assumption
that the pulley is massless and frictionless (see section 7.4 of the text). Consider a cylindrical pulley
of radius R and mass M. Two masses m, < m2 are attached by a massless string. As the pulley
turns, friction in the axle exerts a torque of magnitude t. If the blocks are released from rest, how
long will it take for m2 to hit the floor?
R
M
m2
m1
a. Establish a coordinate
system and draw a free body diagram for the two blocks, list the knowns
and unknowns. (See sections 1.7 and 5.7 of the text on how to draw a correct free body diagram.)
b. Assume the pulley is a rigid body. Draw an extended free body diagram for the pulley. An
extended diagram, often called a torque diagram, shows the point of application of the forces. On
your diagram, label the axis of rotation, the forces which act on the pulley and their distance from
the axis of rotation. Identify any torques caused by those forces and the signs of the torques.
c. Write down Newton's Second Law for m¡ , m2 and the pully. Are there
constraints? If so, what are they? Is the tension on each block the same? Explain why or why not.
(See section 7.3 of the text)
any
acceleration
d. Determine a symbolic expression for the acceleration of m2.
acceleration.
Show that
your
result has units of
e. Suppose the pulley has radius R = 6.0 cm, mass M
= 2.0 kg, the friction on the axle exerts a
of magnitude T = 0.50 Nm, m, = 2.0 kg, m2 = 4.0 kg and d = 1.0 m. If the blocks are
torque
released from rest, how long does it take m2 to reach the floor? Show that your result has units of
time.
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