HARD physics question?

2016-08-02 6:42 am

A spherical body of mass m=10kg and radius r=100mm hangs from a continuous string as shown in the figure. The body is partially submerged in water and angle α= 45 degrees (fixed). If the force of buoyancy is ρVg where ρ=1000 kg/m3 = desnity of water, V is the submerged volume of the body and g is the gravity.

a)Find the tension in the string as a function of the submerged volume V

b) find the maximum and the minimum tension coreesponding to fully and zerosub merged volume of the body respectively

https://postimg.org/image/woc963h2v/

回答 (1)

micatkie

2016-08-02 7:29 am

✔ 最佳答案

Take g = 9.81 m/s²

a)
Upward forces acting on the ball :
Vertical components of the tension = 2 T cos45° (N)
Force of buoyancy =ρVg = 1000 × V × g = 9810 V (N)

Downward force acting on the ball :
Weight of the ball = m g = 10 × g = 98.1 N

When the ball is at rest :
Upward forces acting on the ball = Downward force acting on the ball
2 T cos45° + 9810 V = 98.1

Tension in the string, T = (98.1 - 9810 V) / (2 cos45°)

b)
It should be :
" find the MINIMNUM and the MAXIMUM tension corresponding to fully and zero submerged volume ......"

Volume of the ball = (4/3) × π × (100 × 10⁻³)³ m³

When the ball is fully submerged :
Minimum tension, T = [98.1 - 9810 × (4/3) × π × (100 × 10⁻³)³] / (2 cos45°) = 40.3 N

When the ball is zero submerged :
Maximum tension, T = (98.1 - 0) / (2 cos45°) = 69.4 N

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