Hooke's Law and Spring Constants

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Questions and Answers

What is the elastic potential energy stored in a spring with a spring constant of 240 N/m compressed by 0.0327 m?

0.13 J (correct)

0.08 J

0.10 J

0.15 J

If a 0.0500 kg projectile is launched with a velocity of 2.7 m/s from a spring compressed by 0.030 m, what is the kinetic energy of the projectile?

0.1 J (correct)

0.2 J

0.5 J

What is the maximum speed achieved by a mass of 2.0 kg released from a spring with a constant of 65 N/m stretched to 0.30 m?

2.5 m/s

1.5 m/s

2.0 m/s

1.7 m/s (correct)

What is the acceleration of a mass on a spring when displaced 0.20 m given a spring constant of 65 N/m?

-6.5 m/s² Signup and view all the answers

What is the gravitational potential energy of a 0.80 kg mass at a height of 1 m?

9.81 J Signup and view all the answers

How much work is done to compress a spring with a spring constant of 55 N/m by 0.040 m?

0.044 J Signup and view all the answers

A mass on a horizontal spring follows simple harmonic motion. What forces act on it to maintain this motion?

Restorative forces towards equilibrium Signup and view all the answers

If a spring's compression distance is doubled, how does this affect the elastic potential energy stored in the spring?

Increases by a factor of 4 Signup and view all the answers

What will happen to a spring if too much force is applied?

It may become permanently deformed. Signup and view all the answers

What does Hooke's Law state about the restoring force of a spring?

The restoring force is proportional to the displacement. Signup and view all the answers

How is the elastic potential energy in a spring calculated?

Ep = 1/2 kx² Signup and view all the answers

In a force vs. stretch graph for a spring, what does the slope represent?

The spring constant k. Signup and view all the answers

If the spring constant (k) of a spring is 500 N/m and it is stretched by 0.5 m, what is the elastic force exerted by the spring?

500 N Signup and view all the answers

What concept describes the ability of stored energy in a spring to do work?

Elastic potential energy Signup and view all the answers

If a spring with a spring constant of 240 N/m has a weight of 0.80 kg hanging from it, what is the gravitational force acting on the mass?

4.9 N Signup and view all the answers

What is the spring constant of a spring if a mass of 3.0 kg causes a stretch of 0.05 m?

588 N/m Signup and view all the answers

What is the formula used to relate gravitational potential energy to the maximum height reached by an object released from a compressed spring?

mgh = Kx²/2 Signup and view all the answers

If a ball of mass 0.50 kg is moving with a speed of 1.5 m/s, what is its kinetic energy?

1.125 J Signup and view all the answers

During the compression of a spring, what happens to the elastic potential energy when the spring is released?

It transforms into kinetic energy as the object moves. Signup and view all the answers

What is the acceleration of a 0.020 kg mass when attached to a spring with a spring constant of 220 N/m and displaced 0.030 m?

-110 m/s² Signup and view all the answers

What is the maximum height reached by a toy of mass 0.020 kg when a spring with a spring constant of 220 N/m is compressed 0.030 m?

0.50 m Signup and view all the answers

In simple harmonic motion, when the potential energy is maximum, what is the kinetic energy?

Zero Signup and view all the answers

What is the spring constant of a spring if a mass of 0.50 kg attached to it achieves a maximum speed of 1.5 m/s after compressing it 0.25 m?

18 N/m Signup and view all the answers

What is the kinetic energy of a spring pop-up toy of mass 0.020 kg at the point of release from a spring compressed 0.030 m?

0.098 J Signup and view all the answers

Study Notes

Hooke's Law

A stretched spring stores energy, called elastic potential energy.
A spring's ability to do work when returning to its original position indicates stored energy.
Springs have varying stiffness, indicated by the spring constant (k).

Hooke's Law Lab

A force-vs-stretch graph results in a straight line.
The slope of the graph equals the spring constant (k).
The spring constant (k) conversion from the example given (from data provided) is 10 N/m.
The spring constant (k) conversion from the example given (from the data provided is also 4 N/0.4m which is 10 N/m)

Hooke's Law - Restoring Force

A stretched spring exerts a restoring force to return to its equilibrium position (Newton's Third Law).
Hooke's Law: F = -kx
- F = restoring force
- k = spring constant (N/m)
- x = displacement (m)
Excessive force can permanently deform or break a spring.

Example Calculations - Spring Constant

Example 1: Given a spring constant of 175 N/m and a stretch of 30cm, the elastic force is calculated at 52.5 N.
The calculation of spring constant when given a 2.0 kg mass hanging on a spring stretched 4.0cm from its rest position equals 490 N/m.

Energy in a Spring

Stored energy in a spring is elastic potential energy (Ep).
Formula for elastic potential energy: Ep = ½kx²
- Ep = elastic potential energy (joules)
- k = spring constant (N/m)
- x = displacement (m)
The work done on a spring equals the area under a force-vs-stretch graph

Example Calculations - Energy in a Spring

Example (page 6): A spring with a constant of 240 N/m and a 0.80 kg mass suspended from it has an extension of 0.0327 m and elastic potential energy of 0.13 J
Example (page 7): The work done to compress a spring 4.0 cm with a 55N/m constant is 0.044J.
Example (page 7): A toy gun with a 410 N/m spring compressed 3.0cm and 0.05kg projectile has launch velocity of 2.7m/s.
Example (page 10): A 9.0N/m spring with a .0100kg mass displaced 5.0cm to the right of its rest position shows a -45 m/s² acceleration and a velocity of 1.5 m/s when at rest.
Example (page 10): 0.0189=0.010V² (calculation) with velocity of 1.4m/s, when at the stated displacement.
Example (page 11): A 0.020kg toy with spring constant of 220N/m and 0.030 m compression reaches maximum height of 0.50m.
Example (page 11): A 0.50 Kg ball attached to a horizontal spring and compressed 0.25m from the equilibrium position, is released. A maximum speed of 1.5m/s is calculated and the spring constant is 18 N/m. The speed when 0.125m from its equilibrium position is 1.3 m/s.

Simple Harmonic Motion

Repetitive back-and-forth motion around an equilibrium position.
The force for the motion is directly proportional to the displacement from equilibrium.
Examples include a mass on a horizontal spring.
Example (page 8) and (page 9) demonstrates this motion through calculations, showing the relationship between the displacement and acceleration.

Types of Collisions

Elastic Collisions: Kinetic energy is conserved. Objects bounce apart.
Inelastic Collisions: Kinetic energy is not conserved. Objects usually stick together.
Example (page 13): Elastic vs Inelastic Collision.

Example Calculations - Collisions (Elastic/Inelastic)

Example (page 14): A 1200 kg car traveling East at 25m/s collides with a 1300kg car traveling West at 19m/s and then rebounds at 27m/s. The collision here is Inelastic.
Example (page 14): A 95 kg hockey player traveling East at 2.3m/s collides with a 104kg player traveling West at 1.2 m/s. The final speed of the entangled players is 0.47m/s East. The collision here is also Inelastic .

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Description

Test your understanding of Hooke's Law and the behavior of springs. This quiz covers concepts such as elastic potential energy, restoring force, and calculations related to the spring constant. Dive deeper into the mechanics and applications of springs in physics!