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 the mass of the stone is 1 kg?
Practice Questions
1 question
Q1
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 the mass of the stone is 1 kg?
2 N
4 N
8 N
10 N
Centripetal force = m(v²/r) = 1(4²/2) = 8 N. Tension in the string = 8 N.
Questions & Step-by-step Solutions
1 item
Q
Q: 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 the mass of the stone is 1 kg?
Solution: Centripetal force = m(v²/r) = 1(4²/2) = 8 N. Tension in the string = 8 N.
Steps: 6
Step 1: Identify the given values. The mass of the stone (m) is 1 kg, the speed (v) is 4 m/s, and the radius (r) is 2 m.
Step 2: Use the formula for centripetal force, which is F = m(v²/r). This formula helps us find the force needed to keep the stone moving in a circle.
Step 3: Calculate v² (the speed squared). Here, v = 4 m/s, so v² = 4 * 4 = 16 m²/s².
Step 4: Divide v² by r (the radius). We have v² = 16 m²/s² and r = 2 m, so 16 / 2 = 8 m/s².
Step 5: Multiply the result by the mass (m). We have m = 1 kg, so the centripetal force is 1 kg * 8 m/s² = 8 N.
Step 6: The tension in the string is equal to the centripetal force needed to keep the stone moving in the circle, which is 8 N.
