If a stone is tied to a string and whirled in a horizontal circle of radius 2 m

If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string?

If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string?

Step 1: Identify the formula for centripetal force, which is F_c = mv²/r.
Step 2: Determine the values needed for the formula. We have the radius (r) = 2 m and the speed (v) = 4 m/s.
Step 3: Assume a mass (m) for the stone. In this case, we will assume m = 1 kg.
Step 4: Plug the values into the formula: F_c = 1 kg * (4 m/s)² / 2 m.
Step 5: Calculate (4 m/s)², which is 16 m²/s².
Step 6: Now calculate F_c = 1 kg * 16 m²/s² / 2 m.
Step 7: Divide 16 m²/s² by 2 m, which gives 8 m/s².
Step 8: Since mass is in kg, the result is in Newtons (N). Therefore, the tension in the string is 8 N.

Centripetal Force – The force required to keep an object moving in a circular path, directed towards the center of the circle.
Tension in a String – The force exerted by a string when it is pulled tight by forces acting from opposite ends.
Circular Motion – The motion of an object in a circular path, which requires a net inward force.