Chapter 9: Q. 26 (page 228)

A $35$ -cm-long vertical spring has one end fixed on the floor. Placing a $2.2$ kg physics textbook on the spring compresses it to a length of $29$ cm. What is the spring constant?

Short Answer

Expert verified

The spring constant $k = 360$ N/m

Step by step solution

Step 1. Given Information

A vertical spring with $35$ cm length and a $2.2$ kg of physics textbook compressed it to a length of $29$ cm

Step 2. Hooke's Law

When a spring is compressed, a force is exerted by its material to restore it to its equilibrium position and this force is called restoring force $F_{s p}$ . Hooke's law state the relationship between the restoring force and the vertical displacement $∆ y$

$F_{s p} = - k ∆ y$

where $k$ is the force constant and the negative sign shows the direction

Step 3. Find the spring constant

The book presses against the free end of the spring, so it exerts a force in the negative sign of the restoring due to its weight $m g$ , so the force is given by

$F = F_{s p} m g = - k ∆ y k = - \frac{m g}{∆ y}$

the length of the spring changes from $35$ cm to $29$ cm, we put the values

$k = - \frac{m g}{∆ y} = \frac{(2.2 k g) (9.8 m / s^{2})}{0.29 m - 0.35 m} = 360 N / m$

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A $35$ -cm-long vertical spring has one end fixed on the floor. Placing a $2.2$ kg physics textbook on the spring compresses it to a length of $29$ cm. What is the spring constant?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Hooke's Law

Step 3. Find the spring constant

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A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Hooke's Law

Step 3. Find the spring constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Fundamentals of Physics

Wave Optics

Oscillations

Force

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.

A $35$ -cm-long vertical spring has one end fixed on the floor. Placing a $2.2$ kg physics textbook on the spring compresses it to a length of $29$ cm. What is the spring constant?