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Q. 65

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 418

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Short Answer

On your first trip to Planet you happen to take along a mass, a -long spring, a meter stick, and a stopwatch. You’re curious about the free-fall acceleration on Planet , where ordinary tasks seem easier than on earth, but you can’t find this information in your Visitor’s Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by . You then pull the mass down and release it. With the stopwatch you find that oscillations take . Based on this information, what is ?

The value of on planet is

See the step by step solution

Step by Step Solution

Step 1: Concepts and Principles

The period of oscillation in simple harmonic motion is given by

is independent on amplitude but only on the mass and the force constant

Step 2 : Given data

The mass of the object is

The distance stretched in the spring by mass when the spring is hung from ceiling

The time of oscillation of the mass is

Step 3: Required data

The objective is to determine the value of on planet

Step 4 : Solution

Figure 1 displays the free body diagram of the forces acting on the mass when the spring is hung from the ceiling; is the spring force and is the gravitational force exerted by earth

Step 5 : Solve

As the mass in at rest, so the net force on it must be zero

To find

substituting values

Step 6 : Solve

The period of oscillation of the mass can be obtained from equation

where on the behalf of stop watch measures oscillations

Rearrange and solve for

Substitute value in equation

Step 7: solve  

Solve for

substituting values in it to find out value

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