A 2.0-m long string is tied to a 3.0-kg rock and the rock is twirled around in a circle at a constant speed.The speed of the rock is such that the string makes an angle of 45 degrees with the horizontal.What is the speed of the rock?
A)2.8 m/s
B)4.0 m/s
C)3.7 m/s
D)4.4 m/s
E)5.0 m/s

Question

Quizplus · Accepted Answer

The tension in the string provides the centripetal force keeping the rock moving in a circle. The tension T in the string is given by T = (m*v^2)/r, where m is the mass of the rock, v is its velocity, and r is the radius of the circle (equal to the length of the string). Since the string makes an angle of 45 degrees with the horizontal, the vertical component of the tension balances the weight of the rock, and the horizontal component provides the centripetal force. This gives T*cos(45) = m*g, or T = m*g/cos(45), where g is the acceleration due to gravity. Substituting this expression for T into the equation for centripetal force gives (m*v^2)/r = T*sin(45), or v = sqrt((r*g*tan(45))/m) = sqrt((2*9.81*tan(45))/3) =~ 3.7 m/s. Therefore, the best choice is C.

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