A stone with mass 0.83kg is attached to one end of a string 0.94m long. The string will break if its tension exceeds 62.0N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. (a) Draw a free body diagram of the stone. (b) Find the maximum speed the stone can attain without the string breaking.

icon
Related questions
Question

Please show work and answer all parts

**Problem Description:**

A stone with mass 0.83 kg is attached to one end of a string 0.94 m long. The string will break if its tension exceeds 62.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed.

(a) Draw a free body diagram of the stone.

(b) Find the maximum speed the stone can attain without the string breaking.

**Instructions:**

- **Part (a): Free Body Diagram**
  - Visualize the stone at the center of a circular path.
  - Represent the tension in the string as an arrow pointing radially inward toward the center of the circle.
  - Consider gravitational force acting downward and normal force upward, even though their effects are not felt due to the horizontal motion.

- **Part (b): Maximum Speed Calculation**
  - Use the formula for centripetal force: \( F = \frac{mv^2}{r} \).
  - Set the maximum tension as the centripetal force and solve for \( v \).
  - Plug in the given values: \( m = 0.83 \, \text{kg} \), \( r = 0.94 \, \text{m} \), \( F = 62.0 \, \text{N} \).
  - Calculate the maximum speed \( v \).
Transcribed Image Text:**Problem Description:** A stone with mass 0.83 kg is attached to one end of a string 0.94 m long. The string will break if its tension exceeds 62.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. (a) Draw a free body diagram of the stone. (b) Find the maximum speed the stone can attain without the string breaking. **Instructions:** - **Part (a): Free Body Diagram** - Visualize the stone at the center of a circular path. - Represent the tension in the string as an arrow pointing radially inward toward the center of the circle. - Consider gravitational force acting downward and normal force upward, even though their effects are not felt due to the horizontal motion. - **Part (b): Maximum Speed Calculation** - Use the formula for centripetal force: \( F = \frac{mv^2}{r} \). - Set the maximum tension as the centripetal force and solve for \( v \). - Plug in the given values: \( m = 0.83 \, \text{kg} \), \( r = 0.94 \, \text{m} \), \( F = 62.0 \, \text{N} \). - Calculate the maximum speed \( v \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer