An Atwood\'s machine consists of two masses, mA and mB, which are connected by a

Question

An Atwood's machine consists of two masses, mA and mB, which are connected by a massless inelastic cord that passes over a pulley, see the figure(Figure 1) .

part 1

If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses mA and mB.

Express your answer in terms of the variables mA, mB, I, and appropriate constants.

part 2

Compare to the situation in which the moment of inertia of the pulley is ignored.

Express your answer in terms of the variables mA, mB, and appropriate constants.

An Atwood's machine consists of two masses, mA and mB, which are connected by a massless inelastic cord that passes over a pulley, see the figure(Figure 1) . part 1 If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses mA and mB.

Explanation / Answer

Part A)

For the first mass

mAg - FTA = mAa

FTA = mAg- mAa

For the second mass...

FTB - mBg = mBa

FTB = mBg+ mBa

For the pulley

(FTA - FTB)R = Ia/R

mAg- mAa - mBg- mBa = Ia/R2

mAg - mBg = Ia/R2 + mAa + mBa

mAg - mBg = a(I/R2 + mA + mB)

a = (mAg - mBg)/(I/R2 + mA + mB)

Part B)

The tensions are the same when you ignore the moment of inertia of the pulley...

For the first mass

mAg - FT = mAa

FT = mAg- mAa

For the second mass...

FT - mBg = mBa

FT = mBg+ mBa

mAg- mAa = mBg+ mBa

mAg- mBg = mAa+ mBa

a = (mAg- mBg)/(mA + mB)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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