A ball is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 2 N and the weight of the ball is 3 N. What is the speed of the ball at the highest point if the radius of the circle is 1 m?
Practice Questions
1 question
Q1
A ball is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 2 N and the weight of the ball is 3 N. What is the speed of the ball at the highest point if the radius of the circle is 1 m?
1 m/s
2 m/s
3 m/s
4 m/s
At the highest point, T + mg = mv²/r. 2 N + 3 N = mv²/1. v² = 5, v = √5 ≈ 2.24 m/s.
Questions & Step-by-step Solutions
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Q
Q: A ball is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 2 N and the weight of the ball is 3 N. What is the speed of the ball at the highest point if the radius of the circle is 1 m?
Solution: At the highest point, T + mg = mv²/r. 2 N + 3 N = mv²/1. v² = 5, v = √5 ≈ 2.24 m/s.
Steps: 7
Step 1: Identify the forces acting on the ball at the highest point. The tension in the string (T) is 2 N and the weight of the ball (mg) is 3 N.
Step 2: Write down the equation that relates the forces to the motion of the ball. At the highest point, the sum of the tension and the weight provides the necessary centripetal force: T + mg = mv²/r.
Step 3: Substitute the known values into the equation. Here, T = 2 N, mg = 3 N, and r = 1 m. So, we have: 2 N + 3 N = mv²/1.
Step 4: Simplify the equation. This gives us: 5 N = mv².
Step 5: Since we need to find the speed (v), we can rearrange the equation to solve for v²: v² = 5.
Step 6: Take the square root of both sides to find v: v = √5.
Step 7: Calculate the numerical value of v. √5 is approximately 2.24 m/s.
