# 16.1 Hooke’s law: stress and strain revisited  (Page 4/8)

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## Test prep for ap courses

Which of the following represents the distance (how much ground the particle covers) moved by a particle in a simple harmonic motion in one time period? (Here, A represents the amplitude of the oscillation.)

1. 0 cm
2. A cm
3. 2 A cm
4. 4 A cm

(d)

A spring has a spring constant of 80 N∙m −1 . What is the force required to (a) compress the spring by 5 cm and (b) expand the spring by 15 cm?

In the formula $F\text{\hspace{0.17em}}=\text{\hspace{0.17em}}-kx$ , what does the minus sign indicate?

1. It indicates that the restoring force is in the direction of the displacement.
2. It indicates that the restoring force is in the direction opposite the displacement.
3. It indicates that mechanical energy in the system decreases when a system undergoes oscillation.
4. None of the above

(b)

The splashing of a liquid resembles an oscillation. The restoring force in this scenario will be due to which of the following?

1. Potential energy
2. Kinetic energy
3. Gravity
4. Mechanical energy

## Section summary

• An oscillation is a back and forth motion of an object between two points of deformation.
• An oscillation may create a wave, which is a disturbance that propagates from where it was created.
• The simplest type of oscillations and waves are related to systems that can be described by Hooke’s law:
$F=-\text{kx},$

where $F$ is the restoring force, $x$ is the displacement from equilibrium or deformation, and $k$ is the force constant of the system.

• Elastic potential energy ${\text{PE}}_{\text{el}}$ stored in the deformation of a system that can be described by Hooke’s law is given by
${\text{PE}}_{\text{el}}=\left(1/2\right){\mathit{\text{kx}}}^{2}.$

## Conceptual questions

Describe a system in which elastic potential energy is stored.

## Problems&Exercises

Fish are hung on a spring scale to determine their mass (most fishermen feel no obligation to truthfully report the mass).

(a) What is the force constant of the spring in such a scale if it the spring stretches 8.00 cm for a 10.0 kg load?

(b) What is the mass of a fish that stretches the spring 5.50 cm?

(c) How far apart are the half-kilogram marks on the scale?

(a) $1\text{.}\text{23}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N/m}$

(b) $6\text{.}\text{88 kg}$

(c) $4\text{.00 mm}$

It is weigh-in time for the local under-85-kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke’s law and is depressed 0.75 cm by its maximum load of 120 kg. (a) What is the spring’s effective spring constant? (b) A player stands on the scales and depresses it by 0.48 cm. Is he eligible to play on this under-85 kg team?

One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. (a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s. (b) What force must be exerted to compress the spring?

(a) 889 N/m

(b) 133 N

(a) The springs of a pickup truck act like a single spring with a force constant of $1\text{.}\text{30}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ . By how much will the truck be depressed by its maximum load of 1000 kg?

(b) If the pickup truck has four identical springs, what is the force constant of each?

When an 80.0-kg man stands on a pogo stick, the spring is compressed 0.120 m.

(a) What is the force constant of the spring? (b) Will the spring be compressed more when he hops down the road?

(a) $6\text{.}\text{53}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N/m}$

(b) Yes

A spring has a length of 0.200 m when a 0.300-kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is the unloaded length of the spring?

Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
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Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
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Sphere
e.g. heart Uses 2 W per beat.
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did you solve?
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1.75cm
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my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
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the same behavior thru the prism out or in water bud abbot
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Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
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In what ways does physics affect the society both positively or negatively