Chapter 10: Q. 46 (page 258)

A $1000 k g$ safe is $2.0 m$ above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it $50 c m$ . What is the spring constant of the spring?

Short Answer

Expert verified

The spring constant of the spring is $k = 156, 960 N / m$ .

Step by step solution

Given information

The weight of the safe $= 1000 k g$

The distance between the safe and heavy-duty spring, $h = 2 m$

The safe hits the spring and compresses it

50 c m

Explanation

The potential energy of a mass at height h is taken as $m g h$ . Energy stored in the spring with spring constant k when it is compressed by a distance x is $\frac{1}{2} k x^{2}$ .

The safe hits the spring with KE,

localid="1649411903428" $K E = m g h K E = (1000 k g) \times (9.81 m / s^{2}) \times (2 m) K E = 19620 J$

This energy is stored in the spring when it is compressed. That is

localid="1649411942679" $K E = \frac{1}{2} k x^{2} 19, 620 J = \frac{1}{2} k {(0.50 m)}^{2} k = \frac{2 \times (19, 620 J)}{{(0.50 m)}^{2}} k = 156, 960 N / m$

The energy is conserved. The potential energy of the safe is converted to the energy stored in the spring when the spring is compressed.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A $1000 k g$ safe is $2.0 m$ above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it $50 c m$ . What is the spring constant of the spring?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

Electromagnetism

Dynamics

Waves Physics

Oscillations

Electricity

Study anywhere. Anytime. Across all devices.

A1000kgsafe is 2.0mabove a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50cm. What is the spring constant of the spring?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

Electromagnetism

Dynamics

Waves Physics

Oscillations

Electricity

Study anywhere. Anytime. Across all devices.

A $1000 k g$ safe is $2.0 m$ above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it $50 c m$ . What is the spring constant of the spring?