Question
A stone of mass 500g tied to a rope 50 cm long is whirled at an angular velocity of 12.0 radians per second. Calculate the centripetal force.
Answer
The central force of the stone is 36 Newtons
![A stone of mass 500g tied to a rope 50 cm long](https://physicscalculations.com/wp-content/uploads/2023/03/The-amplitude-of-SHM-y2sin5πt2–√cosπt-is-1-300x300.png)
Explanation
Data: Unrevealed information from the question
Mass of the stone, m = 500 g = (500 / 1000) kg = 0.5 kg
Radius of the circle, r = 50 cm = (50 / 100) m = 0.5 m
Angular velocity, ω = 12 rad/s
Unknown: Unrevealed information from the question
Linear velocity, V = ?
Centripetal force, F = ?
Formula: The equation that will help us solve the problem
Step 1: To find the linear velocity, we will apply the equation below
V = ωr
Step 2: We can use the formulae below to calculate the centripetal force
F = mV2 / r and since V = ωr
We can say that F = mω2r [Which is the formula that will help us find the centripetal force]
Solution
Step 1: If we are to use the first formula, we will start by by finding the linear velocity
V = ωr = 12 x 0.5 = 6 m/s
Therefore, the linear velocity of the stone is 6 m/s
Step 2: We will now apply the formula F = mω2r to find the centripetal force
Hence,
F = mω2r = 0.5 x 122 x 0.5 = 0.5 x 144 x 0.5 = 36 N
Therefore, the centripetal force is 36 Newtons
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