(a) force constant = k ≈ 889 N/m
(b) magnitude of force = F ≈ 133 N
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Further explanation
Let's recall Elastic Potential Energy formula as follows:
[tex]\boxed{E_p = \frac{1}{2}k x^2}[/tex]
where:
Ep = elastic potential energy ( J )
k = spring constant ( N/m )
x = spring extension ( compression ) ( m )
Let us now tackle the problem!
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Given:
mass of bullet = m = 0.0500 kg
speed of bullet = v = 20.0 m/s
compression = x = 0.150 m
Asked:
(a) force constant = k = ?
(b) magnitude of force = F = ?
Solution:
Firstly , we will use Conservation of Energy formula to solve this problem:
[tex]Ep = Ek[/tex]
[tex]\frac{1}{2}k x^2 = \frac{1}{2} m v^2[/tex]
[tex]k x^2 = m v^2[/tex]
[tex]k = m v^2 \div x^2[/tex]
[tex]k = 0.0500 ( 20.0 )^2 \div 0.150^2[/tex]
[tex]\boxed {k \approx 889 \texttt{ N/m}}[/tex]
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Next , we will calculate the magnitude of force by using Hooke's Law as follows:
[tex]F = k x[/tex]
[tex]F = 889 \times 0.150[/tex]
[tex]\boxed {F \approx 133 \texttt{ N}}[/tex]
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Learn more
- Kinetic Energy : https://brainly.com/question/692781
- Acceleration : https://brainly.com/question/2283922
- The Speed of Car : https://brainly.com/question/568302
- Young Modulus : https://brainly.com/question/9202964
- Simple Harmonic Motion : https://brainly.com/question/12069840
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Answer details
Grade: High School
Subject: Physics
Chapter: Elasticity
