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.

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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

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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

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Geometrical and Physical Optics

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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?