Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Read each scenario and then answer the question.

Scenario A: A [tex]3 \frac{N}{m}[/tex] spring is compressed a distance of 1.0 m.
Scenario B: A [tex]6 \frac{N}{m}[/tex] spring is compressed a distance of 0.8 m.
Scenario C: A [tex]9 \frac{N}{m}[/tex] spring is compressed a distance of 0.6 m.
Scenario D: A [tex]12 \frac{N}{m}[/tex] spring is compressed a distance of 0.4 m.

Which scenario generates the most elastic potential energy? [tex]\square[/tex]

Sagot :

GinnyAnswer
To find which scenario generates the most elastic potential energy, we will calculate the elastic potential energy for each scenario using the formula:

[tex]\[ U = \frac{1}{2} k x^2 \][/tex]

where:
- [tex]\( U \)[/tex] is the elastic potential energy,
- [tex]\( k \)[/tex] is the spring constant, and
- [tex]\( x \)[/tex] is the compression distance.

### Scenario A
For a spring with a spring constant [tex]\( k_a = 3 \frac{N}{m} \)[/tex] compressed a distance [tex]\( x_a = 1.0 \)[/tex] m:

[tex]\[ U_a = \frac{1}{2} k_a x_a^2 \][/tex]
[tex]\[ U_a = \frac{1}{2} \times 3 \times (1.0)^2 \][/tex]
[tex]\[ U_a = \frac{3}{2} \times 1 \][/tex]
[tex]\[ U_a = 1.5 \text{ Joules} \][/tex]

### Scenario B
For a spring with a spring constant [tex]\( k_b = 6 \frac{N}{m} \)[/tex] compressed a distance [tex]\( x_b = 0.8 \)[/tex] m:

[tex]\[ U_b = \frac{1}{2} k_b x_b^2 \][/tex]
[tex]\[ U_b = \frac{1}{2} \times 6 \times (0.8)^2 \][/tex]
[tex]\[ U_b = 3 \times 0.64 \][/tex]
[tex]\[ U_b = 1.92 \text{ Joules} \][/tex]

### Scenario C
For a spring with a spring constant [tex]\( k_c = 9 \frac{N}{m} \)[/tex] compressed a distance [tex]\( x_c = 0.6 \)[/tex] m:

[tex]\[ U_c = \frac{1}{2} k_c x_c^2 \][/tex]
[tex]\[ U_c = \frac{1}{2} \times 9 \times (0.6)^2 \][/tex]
[tex]\[ U_c = 4.5 \times 0.36 \][/tex]
[tex]\[ U_c = 1.62 \text{ Joules} \][/tex]

### Scenario D
For a spring with a spring constant [tex]\( k_d = 12 \frac{N}{m} \)[/tex] compressed a distance [tex]\( x_d = 0.4 \)[/tex] m:

[tex]\[ U_d = \frac{1}{2} k_d x_d^2 \][/tex]
[tex]\[ U_d = \frac{1}{2} \times 12 \times (0.4)^2 \][/tex]
[tex]\[ U_d = 6 \times 0.16 \][/tex]
[tex]\[ U_d = 0.96 \text{ Joules} \][/tex]

### Compare the Energies
Now that we have the elastic potential energies for each scenario:
- [tex]\( U_a = 1.5 \)[/tex] Joules
- [tex]\( U_b = 1.92 \)[/tex] Joules
- [tex]\( U_c = 1.62 \)[/tex] Joules
- [tex]\( U_d = 0.96 \)[/tex] Joules

The scenario with the most elastic potential energy is Scenario B with [tex]\( 1.92 \)[/tex] Joules.

Thus, Scenario B generates the most elastic potential energy.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.