Connect with experts and get insightful answers on IDNLearn.com. Ask any question and receive timely, accurate responses from our dedicated community of experts.
This question is incomplete, the complete question is;
A rifle fires a 2.10 × 10⁻² kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.10 × 10⁻² m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.
Answer:
the spring constant is 303.5 N/m
Explanation:
Given the data in the question;
There is a potential energy associated with the spring;
we know that potential energy = kinetic energy
mgh = [tex]\frac{1}{2}[/tex]kx²
where k is the spring constant and x is the compression
as the pallet is fired, the spring gives kinetic energy which is converted into gravitational potential energy
so
m = 2.10 × 10⁻²
g = 9.81 m/s²
h = 6.10 m
x = 9.10 × 10⁻² m
we substitute
mgh = [tex]\frac{1}{2}[/tex]kx²
2.10 × 10⁻² × 9.81 × 6.10 = [tex]\frac{1}{2}[/tex] × K × ( 9.10 × 10⁻² )²
1.256661 = 0.0041405 × K
K = 1.256661 / 0.0041405
K = 303.5 N/m
Therefore, the spring constant is 303.5 N/m