A uniform solid cylinder of mass m_1 = 2.5 kg and radius R = 20 cm is mounted on

Question

A uniform solid cylinder of mass m_1 = 2.5 kg and radius R = 20 cm is mounted on frictionless bearings about a fixes axis through 0. The rotational inertia of the cylinder about the axis is I = 1/2m_1R^2. A block of mass m_2 = 1.2 kg is suspended by a cord that is wrapped around the cylinder as shown. The block is released at time t = 0. a. Draw extended free body diagrams for both the disk (m_1) and the block (m_2). On your free body diagrams, be sure to draw each force at the location that it occurs, draw the forces with reasonably correct relative magnitudes, and label the type of force as well as the object exerting the force.

Explanation / Answer

part b )

For the cylinder:

TR = (1/2)(m1 R^2) alpha

T = m1 R alpha / 2 ...(1)

For the suspended mass:

m2 g - T = m2 a ...(2)

a = R* alpha ...(3)

Eliminating alpha from (1) and (3):

T = m1 a / 2 ...(4)

Eliminating T from (2) and (4):

m2 g - m1 a / 2 = m2 a

2m2 *g = (2m2 + m1)a

a = 2m2* g / (2m2 + m1)

a = 4.8 m/s^2

T = m1 m2 g / (2m2 + m1).

T = 6 N

part c )

m2*g*h = 1/2mv^2 + /12*Iw^2

v = rw

w = sqrt(2*m2*g*h/[m2/2 + m1/4 ]

w = 4.8 rad/s

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