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Troyanec [42]
3 years ago
10

Two masses —m1 and m2— are connected by light cables to the perimeters of two cylinders of radii r1 and r2 respectively, as show

n in the diagram. The cylinders are rigidly connected to each other on a common axle. The moment of inertia of the pair of cylinders is =45 kgm^2. Also, r1= 0.5 m, r2 = 1.5 m, and m1 = 20 kg. Note: m1 is hanging from the small cylinder, and m2 is hanging from the large cylinder. Determine m2 such that the system will remain in equilibrium. The mass m2 is removed and the system is released from. Determine the angular acceleration of the cylinders. Determine the tension in the cable supporting m1. Determine the linear speed of m1 at the time it has descended 1 m.
Physics
1 answer:
Aleksandr [31]3 years ago
7 0

Answer:

Part a)

Mass of m2 is given as

m_2 = \frac{20}{3} kg

Part b)

Angular acceleration is given as

\alpha = 1.96 rad/s^2

Part c)

Tension in the rope is given as

T = 176.6 N

Explanation:

Part a)

When m1 and m2 both connected to the cylinder then the system is at rest

so we can use torque balance here

m_1g r_1 = m_2 g r_2

20 g(0.5) = m_2 g(1.5)

10 = 1.5 m_2

m_2 = \frac{20}{3} kg

Part b)

When block m_2 is removed then system becomes unstable

so force equation of mass m1

m_1g - T = m_1 a

also we have

T r_1 = I\alpha

now we have

m_1g = \frac{I a}{r_1^2} + m_1 a

a = \frac{m_1g}{\frac{I}{r_1^2} + m_1}

a = \frac{20 (9.81)}{\frac{45}{0.5^2} + 20}

a = 0.981 m/s^2

so angular acceleration is given as

\alpha = \frac{a}{r_1}

\alpha = \frac{0.981}{0.5}

\alpha = 1.96 rad/s^2

Part c)

Tension in the rope is given as

T = \frac{I\alpha}{r_1}

T = \frac{45 (1.96)}{0.5}

T = 176.6 N

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