Exercise 10.16 A 12.0-kg box resting on a horizontal, frictionless surface is at

Question

Exercise 10.16 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 figure (Figure 1)). The pulley has the shape of a uniform solid disk of mass 1.60 kg and diameter 0.440 m. Part A After the system is released, find the horizontal tension in the wire. |Th|= N After the system is released, find the vertical tension in the wire. |Tv|= N Part C After the system is released, find the acceleration of the box. a= m/s^2 Part D After the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley. Express your answers separated by a comma. Fx,Fy= N

Explanation / Answer

here ,

let the acceleration of the system is a

using second law of motion

a = net force/effective mass

a = (5 * 9.8)/(5 + 12 + Ip/r^2)

a = (5 * 9.8)/(5 + 12 + 0.5 * 1.6 * r^2/r^2)

a = 2.75 m/s^2

for the horizontal tension ,

Th = 2.75 * 12

Th = 33 N

the tension in the horizontal wire is 33 N

b)

for the mass 5 Kg

Using second law of motion

5 * 9.8 - Tv = 5 * 2.75

Tv = 35.25 N

the tension in the vertical wire is 35.3 N
part c)

acceleration of the box is 2.75 m/s^2

d)

as the pulley is stationay ,

Fx = Th = 33 N

Fy = Tv = 35.3 N

the force in the components is Fx , Fy = 33 N , 35.3 N

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