A hockey puck with mass 180 g is attached to a rope of length 71.0 cm and swung in a horizontal circle against the ice at a rate of 89.0 rpm. Assuming the ice is frictionless, what is the tension in the rope? 2.01×103 N 4.00×104 N 1.01×103 N 11.1 N
Question
A hockey puck with mass 180 g is attached to a rope of length 71.0 cm and swung in a horizontal circle against the ice at a rate of 89.0 rpm. Assuming the ice is frictionless, what is the tension in the rope? 2.01×103 N 4.00×104 N 1.01×103 N 11.1 N
Solution
To solve this problem, we need to use the formula for centripetal force, which is F = m * ω² * r, where m is the mass, ω is the angular velocity, and r is the radius.
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First, convert the mass from grams to kilograms: 180 g = 0.18 kg.
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Convert the length of the rope from cm to meters: 71.0 cm = 0.71 m.
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Convert the rate from rpm to rad/s. There are 2π radians in a circle and 60 seconds in a minute, so 89.0 rpm = 89 * 2π / 60 = 9.35 rad/s.
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Now, substitute these values into the formula: F = 0.18 kg * (9.35 rad/s)² * 0.71 m = 11.1 N.
So, the tension in the rope is 11.1 N.
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