You tie a 1 kg rock to a 1.5 meter long string and then twirl it around your hea

Question

You tie a 1 kg rock to a 1.5 meter long string and then twirl it around your head in a circular path. As you twirl the rock, your lab partner measures the angle the string makes with the horizontal to be 17º (below the horizontal).

Part B What is the tension in the rope? In Newtons

Part C What is the centripetal acceleration that the ball experiences? In m/s2

Part D What is the radius of the circle that the rock moves in? In m

Part E What is the speed of the rock as it moves around the circular path? In m/s

Explanation / Answer

Here ,

theta = 17 degree

mass of rock , m = 1 kg

length of string ,L = 1.5 m

let the tension in the rope is T

balancing the vertical forces on the rock

T * sin(17) = m *g

T * sin(17) = 1 * 9.8

T = 33.51 N

the tension in the rope is 33.51 N

part C)

Now , for the cetripetal acceleration , using second law of motion

T * cos(17) = m * a

33.51 * cos(17) = 1 * a

a = 32.1 m/s^2

the centripetal acceleration of the ball is 32.1 m/s^2

part D)

Now ,radius of circle = L * cos(17)

radius of circle = 1.5 * cos(17)

radius of circle = 1.434 m

the radius of circle is 1.434 m

part E)

let the speed of rock is v

centripetal acceleration = v^2/r

32.1 = v^2/1.434

v = 6.79 m/s

the speed of the rock is 6.79 m/s

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