An green hoop with mass m h = 2.5 kg and radius R h = 0.17 m hangs from a string

Question

An green hoop with mass mh = 2.5 kg and radius Rh = 0.17 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.2 kg and radius Rd = 0.08 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 4.2 kg and radius Rs= 0.2 m. The system is released from rest.

1) What is magnitude of the linear acceleration of the hoop?

2) What is magnitude of the linear acceleration of the sphere?

3) What is the magnitude of the angular acceleration of the disk pulley?

4) What is the magnitude of the angular acceleration of the sphere?

5) What is the tension in the string between the sphere and disk pulley?

6) What is the tension in the string between the hoop and disk pulley?

7) The green hoop falls a distance d = 1.51 m. (After being released from rest.)

How much time does the hoop take to fall 1.51 m?

8) What is the magnitude of the velocity of the green hoop after it has dropped 1.51 m?

9) What is the magnitude of the final angular speed of the orange sphere (after the green hoop has fallen the 1.51 m)?

Explanation / Answer

1.)

a = F / m

a = 2.5 * 9.8 / (2.5 + 1/2*2.2 + 7/5*4.2)

a = 24.5 / 9.48 = 2.58 m/s^2

2.)

linear acceleration of sphere is 2.58 m/s^2

3.)

angular acceleration = a/R

alpha = 2.58 / 0.08 = 32.25 rad/s^2

4.)

angular acceleration of sphere

alpha = 2.58 / 0.2 = 12.9 rad/s^2

5.)

tension between pulley and sphere = (7/5) * 4.2 * 2.58 = 15.17 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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