A steel ball (density = 7860 k g / m 3 ) with a diameter of 7.5 c m is tied to a

Question

A steel ball (density = 7860kg/m3) with a diameter of 7.5 cm is tied to an aluminum wire 80 cm long and 2.1 mm in diameter. The ball is whirled about in a vertical circle with a tangential speed of 8.0 m/s at the top of the circle and 9.2 m/s at the bottom of the circle.
Part A Find the amount of stretch in the wire at the top of the circle. Express your answer using two significant figures.
Part B Find the amount of stretch in the wire at the bottom of the circle. Express your answer using two significant figures.
A steel ball (density = 7860kg/m3) with a diameter of 7.5 cm is tied to an aluminum wire 80 cm long and 2.1 mm in diameter. The ball is whirled about in a vertical circle with a tangential speed of 8.0 m/s at the top of the circle and 9.2 m/s at the bottom of the circle.
Part A Find the amount of stretch in the wire at the top of the circle. Express your answer using two significant figures.
Part B Find the amount of stretch in the wire at the bottom of the circle. Express your answer using two significant figures.
A steel ball (density = 7860kg/m3) with a diameter of 7.5 cm is tied to an aluminum wire 80 cm long and 2.1 mm in diameter. The ball is whirled about in a vertical circle with a tangential speed of 8.0 m/s at the top of the circle and 9.2 m/s at the bottom of the circle.
A steel ball (density = 7860kg/m3) with a diameter of 7.5 cm is tied to an aluminum wire 80 cm long and 2.1 mm in diameter. The ball is whirled about in a vertical circle with a tangential speed of 8.0 m/s at the top of the circle and 9.2 m/s at the bottom of the circle.
A steel ball (density = 7860kg/m3) with a diameter of 7.5 cm is tied to an aluminum wire 80 cm long and 2.1 mm in diameter. The ball is whirled about in a vertical circle with a tangential speed of 8.0 m/s at the top of the circle and 9.2 m/s at the bottom of the circle.
Part A Find the amount of stretch in the wire at the top of the circle. Express your answer using two significant figures.
Part B Find the amount of stretch in the wire at the bottom of the circle. Express your answer using two significant figures.
Part A Find the amount of stretch in the wire at the top of the circle. Express your answer using two significant figures.
Part A Find the amount of stretch in the wire at the top of the circle. Express your answer using two significant figures.
Part B Find the amount of stretch in the wire at the bottom of the circle. Express your answer using two significant figures.
Part B Find the amount of stretch in the wire at the bottom of the circle. Express your answer using two significant figures.

Explanation / Answer

Volume of ball = 4/3 pi r^3 = (4/3) x pi x (3.75 x 10^-2)^3 = 0.000220893233 m^3

Mass of ball = rho x volume = 7860 x 0.000220893233 = 1.73 Kg

Part A) At top

mv^2 / r = T + mg

T = mv^2 / r - mg

T = ((1.73 x 8^2) / .8) - (1.73 x 9.8)

T = 121.44 N

Part (B) At bottom

T = mv^2 / r + mg

T = ((1.73 x 9.2^2) / .8) + (1.73 x 9.8)

T = 199.98 N

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