Chapter 9: Q.56 (page 230)

When a $65 k g$ cheerleader stands on a vertical spring, the spring compresses by $5.5 c m$ . When a second cheerleader stands on the shoulders of the first, the spring compresses an additional $4.5 c m$ . What is the mass of the second cheerleader?

Short Answer

Expert verified

The mass of second cheerleader is $53 k g$ .

Step by step solution

Content Introduction

Hooke's law says that the force applied on spring is directly proportional to deformation of spring.

$F_{s p} α x F_{s p} = k x$

Here, $F_{s p}$ is force applied on spring, $k$ is spring constant, $x$ is deformation of spring.

Content Explanation

Let mass of first cheerleader is $m_{1}$ and mass of second cheerleader is $m_{2}$ .

The value of spring constant when force applied by first cheerleader during compression is $5.5 c m$

$m_{1} g = k x (65 k g) (9.81 m / s^{2}) = k (5.5 c m) (\frac{1 m}{100 c m}) k = 116 \times 10^{2} N / m$

Total force applied on spring is

$(m_{1} + m_{2}) g = k x (65 k g + m_{2}) (9.81 m / s^{2}) = (116 \times 10^{2} N / m) (10.0 c m) (\frac{1 m}{100 c m}) (65 k g + m_{2}) = 118 k g m_{2} = 53 k g$

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When a $65 k g$ cheerleader stands on a vertical spring, the spring compresses by $5.5 c m$ . When a second cheerleader stands on the shoulders of the first, the spring compresses an additional $4.5 c m$ . What is the mass of the second cheerleader?

Short Answer

Step by step solution

Content Introduction

Content Explanation

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When a 65kg cheerleader stands on a vertical spring, the spring compresses by 5.5cm. When a second cheerleader stands on the shoulders of the first, the spring compresses an additional 4.5cm. What is the mass of the second cheerleader?

Short Answer

Step by step solution

Content Introduction

Content Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Electrostatics

Quantum Physics

Circular Motion and Gravitation

Turning Points in Physics

Linear Momentum

Study anywhere. Anytime. Across all devices.

When a $65 k g$ cheerleader stands on a vertical spring, the spring compresses by $5.5 c m$ . When a second cheerleader stands on the shoulders of the first, the spring compresses an additional $4.5 c m$ . What is the mass of the second cheerleader?