A rope iswrapped around a wheel of diameter, 50 cm. The wheel ismounted with fri

Question

A rope iswrapped around a wheel of diameter, 50 cm. The wheel ismounted with frictionless bearings on an axle through itscenter. A block of 15 kg is suspended from the end of therope. When the system is released from rest the block falls5.0 m in 2.0 s.

a.       (5 points) What is thelinear acceleration of the falling block?

b.     (5 points) What is the angular acceleration of the wheel, assumingthe rope doesn’t slip on the wheel?

c.       (5 points) What is thetension in the rope?

d.     (5points) What is the moment of inertia of the wheel? Note,this should be calculated from data in the problem and not from theformula for I of a disk or a hoop.

Please Show All formulas and workused to get the answer

Explanation / Answer

A rope iswrapped around a wheel of diameter, 50 cm. The wheel ismounted with frictionless bearings on an axle through itscenter. A block of 15 kg is suspended from the end of therope. When the system is released from rest the block falls5.0 m in 2.0 s.

a.     What is the linear acceleration of the falling block?

a=2g/3==19.6/3=6.533m/sec2

b.   What is the angularacceleration of the wheel, assuming the rope doesn’t slip onthe wheel?

       a=r

       so angularacceleration==6.533/0.25=26.13rad/sec2

a

c.      

What is the tension in therope?

     T=mg/3=15*9.8/3=49N

d.     What is the moment of inertia of the wheel?

T     T*r=I*

        soI=49*0.25/26.13=0.4688kgm2

P

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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