Q. 43

Expert-verified
Found in: Page 417

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in FIGURE.a. What is her mass if the spring constant is b. What is her speed when the spring's length is

a. The mass spring constant is .

b. The speed is .

See the step by step solution

Step 1: Calculation for mass (part a)

a.

In simple harmonic motion, the period of an oscillator is given by

From figure,

So,

Step 2: Calculation for area and frequency (part b)

b.

From figure,

Area is,

Angular frequency,

Step 3: Calculation for time part (b) solution

b.

Maximum displacement is,

Where

Step 4: Calculation for speed part (b) solution

b.

Speed is,

Speed has magnitude velocity of ,

So,