A 12.0 kg box resting on a horizontal, frictionless surface is attached to a 5.0

Question

A 12.0 kg box resting on a horizontal, frictionless surface is attached to a 5.00 kg weight by a thin, light wire that passes without slippage over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 1.70 kg and diameter .600 m.

A. What is the horizontal tension?

B. What is the vertical tension?

C. After the system is released, find the acceleration of the box.

D. After the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley.

A 12.0 kg box resting on a horizontal, frictionless surface is attached to a 5.00 kg weight by a thin, light wire that passes without slippage over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 1.70 kg and diameter .600 m. A. What is the horizontal tension? B. What is the vertical tension? C. After the system is released, find the acceleration of the box. D. After the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley.

Explanation / Answer

5g - Tv = 5a

(Tv - Th) x r = (mr^2 /2) x (a/r)

Tv - Th = 1.70a/2   

Th = 12a

add all of them,

5g = (5 + 1.70/2 + 12)a

a =2.74 m/s2 ................Ans(c)

A. Th = 12a =12 x 2.74 =32.94 N

B. Tv = 5( g-a) = 35.35 N

C. a =2.74 m/s2

D. T_hori = Th = 32.94 N

R_vertical = Tv = 35.35 N

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