A string under a tension of 50.0 N is used to whirl a rock...

Name: Problem 39, Chapter 6: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-06-04T23:51:46-08:00
Duration: 1 min 49 s
Channel: Luis Mendoza
Description: A string under a tension of 50.0 N is used to whirl a rock in a horizontal circle of radius 2.50 m at a speed of 20.4 m/s on a frictionless surface as shown in Figure P6.39. As the string is pulled in, the speed of the rock increases. When the string is 1.00 m long and the speed of the rock is 51.0 m/s, the string breaks. What is the breaking strength, in newtons, of the string?

A string under a tension of 50.0 N is used to whirl a rock in a horizontal circle of radius 2.50 m at a speed of 20.4 m/s on a frictionless surface as shown in Figure P6.39. As the string is pulled in, the speed of the rock increases. When the string is 1.00 m long and the speed of the rock is 51.0 m/s, the string breaks. What is the breaking strength, in newtons, of the string?

Key Concepts

Centripetal Force

In uniform circular motion, a net inward force—called the centripetal force—is required to keep an object moving along a circular path. This force is given by the formula F = m v²/r, where m is the object's mass, v is its speed, and r is the radius of the circle. This concept is crucial because the increasing speed of the rock as the string is pulled in directly causes an increase in the required centripetal force, which in turn is provided by the tension in the string.

Tension in Circular Motion

The tension in the string acts as the centripetal force that keeps the rock in circular motion. Initially, a known tension provides the balance for a particular speed and radius, allowing the determination of the rock’s mass. As the radius decreases and the speed increases (while angular momentum is conserved), the tension increases according to the relation F = m v²/r. This understanding is essential for determining when the force exceeds the string’s breaking strength.

Conservation of Angular Momentum

In the absence of external torques, the angular momentum of an object undergoing circular motion remains constant. When the string is pulled inward, the decrease in radius causes an increase in speed so that the product mvr remains constant. This principle explains why the rock’s speed increases as the radius decreases and is indirectly also tied to the increase in centripetal force (and tension) responsible for reaching and eventually exceeding the string’s breaking strength.

Transcript

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