A very light, strong string is wound around a pulley and attached to a large blo

Question

A very light, strong string is wound around a pulley and attached to a large block, as shown in the figure. The block has mass M=2 kg and can slide without friction on a plane that is at an angle of 30 degrees. The pulley is a uniform cylinder of mass m=.5 kg and radius r=5 cm rotating about a frictionless axle. When the pulley is released, the block stats sliding down the incline, unwinding the string from the rim of the pulley.

What is th magnitude of the angular acceleration of the pulley?

What is the tension in the string?

What is the speed of the block when it is .3 m from where it started at rest?

Explanation / Answer

A)

by using law of motion

the force on the block is,

Ma=Mg*sin(theta)-F .......(1) ( here F is tension force)

and

for the pulley

torque T=I*alpa

F*r=m*r^2*(a/r)

F*r=m*r^2*(a/r)

F=m*a........ (2)

now,

from (1) and (2)

Ma=Mg*sin(theta)-ma

a=Mg*sin(theta)/(m+M)

=2*9.8*sin(30)/(2+0.5)

a=3.92 m/sec^2

now,

alpa=a/r

=3.92/0.05

=78.4 rad/sec^2

B)

tension F=m*a

=0.5*3.92

F=1.96 N

c)

v=sqrt(2*a*s)

v=sqrt(2*3.92*0.3)

v=1.534 m/sec

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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