Question

An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes...

An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley. If the pulley has radius and moment of inertia 1/2 MR^2 about its axle. Determine the acceleration if masses m1 and m2. Compare the situation in which moment of inertia is ignored

Homework Answers

Answer #1

let tension in string connecting the mass m2 is T2 and tension in string connecting to mass m1 is T1.

let acceleration of the system be a m/s^2.

assume m2> m1

writing force equation for m2:

m2*g-T2=m2*a

==>T2+m2*a=m2*g....(1)

writing force equation for the pulley:

torque=moment of inertia*angular acceleration

==>T2*R-T1*R=0.5*M*R^2*(a/R)=0.5*M*a*R

==>T2-T1=0.5*M*a....(2)

writing force equation for mass m1:

T1-m1*g=m1*a

==>T1-m1*a=m1*g...(3)

from equation 1, T2=m2*g-m2*a

from equation 2, T1=m1*g+m1*a

using these in equation 2:

m2*g-m1*g-m2*a-m1*a=0.5*M*a

==>(m2-m1)*g=(0.5*M+m1+m2)*a

==>a=(m2-m1)*g/(ma+m2+0.5*M)

when moment of inertia is ingored,

acceleration becomes (m2-m1)*g/(m1+m2)

so acceleration in case of pulley with moment of inertia is lesser.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes...
An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley. If the pulley is a disk of radius R and mass M, find the acceleration of the masses. Express your answer in terms of the variables m1, m2, R, M, and appropriate constants.
Two blocks with masses M1 and M2 are connected by a massless string that passes over...
Two blocks with masses M1 and M2 are connected by a massless string that passes over a massless pulley as shown. M1 has a mass of 2.25 kg and is on an incline of 49.5° with coefficient of kinetic friction ?1 = 0.205. M2 has a mass of 5.45 kg and is on an incline of 31.5° with coefficient of kinetic friction ?2 = 0.105. Find the magnitude of the acceleration of M2 down the incline.
An Atwood's machine consists of blocks of masses m1 = 12.0 kg and m2 = 22.0...
An Atwood's machine consists of blocks of masses m1 = 12.0 kg and m2 = 22.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 7.60 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping. Two objects, blocks labeled m1 and m2, are connected to a cord which is hung...
Two blocks with masses M1 and M2 are connected by a massless string that passes over...
Two blocks with masses M1 and M2 are connected by a massless string that passes over a massless pulley as shown. M1 has a mass of 2.25 kg and is on an incline of θ1=46.5∘ with coefficient of kinetic friction μ1=0.205. M2 has a mass of 6.05 kg and is on an incline of θ2=33.5∘ with coefficient of kinetic friction μ2=0.105. The two‑block system is in motion with the block of mass M2 sliding down the ramp. Find the magnitude...
An Atwood's machine consists of blocks of masses m1 = 13.0 kg and m2 = 19.0...
An Atwood's machine consists of blocks of masses m1 = 13.0 kg and m2 = 19.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 9.20 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping. (a) Why must the tension T2 be greater than the tension T1? This answer has...
A mass m1 is connected by a light string that passes over a pulley of mass...
A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 1.00 kg, m2 is 2.00 kg, and M is 4.00 kg, then what is the tension in the string...
Two masses M1 and M2 are connected by an inextensible flexible massless string. The mass rests...
Two masses M1 and M2 are connected by an inextensible flexible massless string. The mass rests on a table with frictional co-efficient 0.2. The string passes over a smooth fixed pulley as shown. Initially the string is slack The mass M2 is allowed to fall freely from rest. The string becomes taught when the mass M2 falls through 50 cm. The two masses subsequently move with common velocity. Determine how far mass M1 will travel on the table before coming...
Two packing crates of masses m1 = 10.0 kg and m2 = 4.70 kg are connected...
Two packing crates of masses m1 = 10.0 kg and m2 = 4.70 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 4.70-kg crate lies on a smooth incline of angle 35.0°. Find the following. Two crates are connected to each other by a string that passes over a pulley, which is attached to the top corner of a wedge. The crate of mass m1 hangs freely below the pulley....
Two objects with masses of m1 = 3.90 kg and m2 = 5.70 kg are connected...
Two objects with masses of m1 = 3.90 kg and m2 = 5.70 kg are connected by a light string that passes over a frictionless pulley, as in the figure below. A string passes over a pulley which is suspended from a horizontal surface. A circular object of mass m1 and a rectangular object of m2 are, respectively, attached to the left and right ends of the string. (a) Determine the tension in the string. (Enter the magnitude only. Due...
Two masses are connected by a string that passes over a pulley. The mass m1 is...
Two masses are connected by a string that passes over a pulley. The mass m1 is 9.2 kg, and the mass m2 is 1.6 kg. When the masses are simultaneously released from rest, what is the magnitude of their acceleration (in m/s2)? Neglect any friction. [Note: if you need to enter a number in scientific notation, use 'e'. For example, 1200 = 1.2e3 and 0.0012 = 1.2e-3. Include several decimal places in your calculations and your answer to avoid rounding...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT