AP 1 Energy with Springs

The diagram shows the same spring being stretched at different lengths using different masses. At which length does the spring have the MOST potential energy?

• length A

• length B

• length C

• length D

Answer explanation

The potential energy in a spring is given by the formula PE = 1/2 k x^2, where x is the stretch length. As the spring is stretched further, the potential energy increases. Therefore, at length D, the spring has the most potential energy.

Tags

NGSS.HS-PS3-1

NGSS.HS-PS3-2

What is energy conversion?

• one type of energy changing to another type of energy

• energy in one object going into another object

• energy units changing

• energy units staying the same

Answer explanation

Energy conversion refers to the process where one type of energy changes to another type of energy, such as kinetic energy transforming into potential energy. This is the correct definition, distinguishing it from other options.

Tags

NGSS.HS-PS3-3

What is potential energy?

• The energy an object has due to its position or condition.

• The energy an object has due to its motion.

• The energy an object has due to its chemical composition.

• The energy as object has due to its atomic structure.

Answer explanation

Potential energy is defined as the energy an object possesses due to its position or condition, such as height above the ground. This distinguishes it from kinetic energy, which is related to motion.

Tags

NGSS.HS-PS3-2

Elastic potential energy is energy stored in an object, such as a spring, due to the object being stretched or compressed. In which position is it most likely that the spring has lost its elastic potential energy?

• W

• Y

• X

• Z

Tags

NGSS.MS-PS3-2

Elastic Potential Energy is _____________________________________.

• the ability of a material to return to its original shape after it has been stretched or deformed.

• potential energy that is stored due to the deformation of an elastic object, such as a stretched spring.

• energy stored in the bonds of chemical compounds. Chemical energy is released during chemical reactions.

• the energy contained within a system that is responsible for its temperature.

• the flow of thermal energy.

Answer explanation

Elastic Potential Energy refers to the potential energy stored in an elastic object when it is deformed, such as when a spring is stretched. This energy is released when the object returns to its original shape.

Tags

NGSS.HS-PS3-3

A spring has a spring constant of 330 N/m.  How far is the spring compressed if 150 N of force are used?

• 2.2 m

• 0.0014 m

• 5.0 m

• 0.45 m

Answer explanation

Using Hooke's Law, F = kx, where F is the force, k is the spring constant, and x is the compression. Rearranging gives x = F/k. Substituting F = 150 N and k = 330 N/m, we find x = 150/330 = 0.45 m.

What force should be applied to compress a spring by 0.013 m if its spring constant is k = 1900 N/m?

• 1880 N

• 24.7 N

• 1900 N

• 0.127 N

Answer explanation

To find the force (F) needed to compress a spring, use Hooke's Law: F = k * x. Here, k = 1900 N/m and x = 0.013 m. Thus, F = 1900 * 0.013 = 24.7 N. Therefore, the correct answer is 24.7 N.

Which of the following is a true statement regarding springs?

• The higher the value of the spring constant, the stiffer the spring.  

• In Hooke's law, the force exerted by the spring acts in the same direction as displacement.  

• Springs are designed to provide unpredictable variations in force.  

• The force exerted by a spring has a quadratic relationship with the displacement form equilibrium.  

Answer explanation

The correct statement is that the higher the value of the spring constant, the stiffer the spring. This means a spring with a larger constant will resist deformation more than one with a smaller constant.

Which of the following springs is the stiffest?

• A spring that requires a froce of 2000 N to compress it by 6.8 m.

• A spring that requires a force of 4000 N to stretch it by 9.0 m. 

• A spring that requires a force of 8000 N to compress it by 45 m.  

• A spring that requires a force of 4800 N to stretch it by 14 m.

Answer explanation

The stiffness of a spring is determined by the force required per unit displacement (k = F/x). The spring requiring 4000 N for 9.0 m has the highest stiffness (k = 444.44 N/m), making it the stiffest.

What Quantity can you calculate from the graph and give the magnitude of that quantity.  

• distance 4.5 m

• Force 15 N

• spring constant 20 N/m

• spring constant 200 N/m

Answer explanation

The graph likely represents a force vs. extension relationship for a spring. The slope of this graph gives the spring constant. The correct choice, 20 N/m, indicates the spring's stiffness based on the graph's data.