A solid globe of mass M and radius R can rotate about its axis. A block of mass

Question

A solid globe of mass M and radius R can rotate about its axis. A block of mass m is attached by a massless-string/pulley system as shown. As the block falls it causes the globe to spin. If the block starts at rest, at what speed does the block n the ground after it falls a distance h? State your answer in terms of the given variables: M, R, m, h Solve this problem using two different methods. Method 1: Use the concepts of forces, torques and accelerations to solve the pro step of the Problem Solving Strategies that we developed last term in blem. Make sure that you clearly use each Ph 211 along with the "twists" we add this term Problem solving steps a) Draw a picture! Include a "good" coordinate system. b) Draw a FBD c) If a body is being "torqued", draw a Torque Diagram. d) See casieI ou caYL servai aw to make your f) Create an equation using Faet manet for every body in the problem. g) Create an equation using tnet Ionet for every torqued body in the problem. h) Always check to see if you have constant accelerations or changing accelerations.

Explanation / Answer

According to the concept of the rigid body in dynamics

Using conservation of energy principle

We have

Fall in PE of the block=gain in KE of the block +rotational kinetic energy of the solid globe

mgh=1/2mv^2+1/2Iw^2

mgh=1/2mv^2+1/2(2MR^2/3)*(v/R)^2

mgh=1/2mv^2+1/2(2MRv^2/3)

mgh=(m/2+MR/3)v^2

mgh/{m/2+MR/3}=v^2

v=[mgh/{m/2+MR/3}]^1/2

Therefore the speed of the block fallen

V=[mgh/{m/2+MR/3}]^1/2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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