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A piece of modern sculpture consists of an 8.0-m-long, 150 kg stainless steel bar passing diametrically through a 50 kg copper sphere. The center of the sphere is 2.0 m from one end of the bar. To be mounted for display, the bar is oriented vertically, with the copper sphere at the lower end, then tilted 35° from vertical and held in place by one horizontal steel cable attached to the bar 2.0 m from the top end. What is the tension in the cable?

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temdan2001

Answer: Tension T = 801N

Explanation: Given that

The mass of the bar Mb = 150kg

Length L = 8m

Mass of the sphere  = 50kg

Radius  = 2m

Cable distance l = 6m

Angle Ø = 35° 

From the figure attached,

The weight of the sphere  = mg

= 490N

Angle Ø = 90 + 55 = 145 degree

Torque(τ)  = rFsinø

Torque  = 2 × 490sin145

Torque(τ) =  562Nm

The weight of the steel bar = mg

= 1470 N

Radius r = 8/2 = 4m

Torque(τ) = rFsinØ = 4×1470sin145

Torque = 3373Nm

The tension on the rope is at angle

Ø = -(180 - 55) = -125 degree

The torque caused by the tension T will be

Torque(τ) = 6Tsin(-125) = -4.91T

The total Torque(τ) = 0 since the system is in equilibrium. Therefore,

τs + τb + τt + τn = 0

Where τn = 0 since the force on normal force = 0

562 + 3373 - 4.91T + 0 = 0

4.91T = 3935

T = 3935/4.91

T = 801N

Ver imagen temdan2001
batolisis

The Tension in the cable is = 801 N

Given data :

Length of  stainless bar = 8 m

Mass of stainless bar = 150 kg

Mass of copper sphere = 50 kg

Radius of sphere = 2.0 m

Ø = 35°

length of cable / cable distance = 6 m

Determine the tension in the cable

First step : Calculate the weight of the sphere and the weight of steel bar

Weight of sphere ( mg )  = 50 * 9.81 ≈ 490 N

angle = 90 + ( 90 - 35 ) = 145°

Torque (τs )   = r*F*sinØ

                      = 2 * 490 * sin 145°  = 562 Nm

Weight of stainless steel bar ( mg ) = 150 * 9.81 ≈ 1470 N

Radius of steel bar ( r ) = 8 / 2 = 4m

Torque ( τb ) = r * F * sinØ

                     = 4 * 1470 * sin 145° = 3373 Nm

Final step : Determine the tension in the cable

Ø =  - ( 180 - 55) = -125°

Torque ( τt ) =  6*T*sin (-125°) = - 4.91 T

Given that the system is in equilibrium the Total torque ( T ) = 0

τs + τb + τt + τn = 0

562 + 3373 - 4.91T + 0 = 0

4.91 T = 3935

∴ T = 801 N

Hence we can conclude that Tension in the cable is 801 N

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