- #1
henrco
- 47
- 2
Hi,
Could you please help me determine if I've worked this problem out correctly.
1. Homework Statement
A 2.86-kg object on a frictionless horizontal surface oscillates at the end of a spring with an amplitude of
7.81 cm. Its maximum acceleration is 3.74 m/s2.
Calculate the total mechanical energy.
1) Total Mechanical Energy: E = 0.5 k A^2
2) Spring Constant: k = m w^2 (where w = angular velocity)
3) Acceleration : a = -w^2 x
Given the Amplitude A, we must calculate the spring constant k to calc the total mechanical energy.
First find w using formula 3)
w = - sqr( a / x)
w = - sqr(3.74 / 0.0781)
w = - 6.92
Now substitute k in formula 1 with formula 2 to calculate the total mechanical energy.
E = 0.5 (m w^2) A^2
E= 0.5 (2.86) (-6.92)^2 (0.0781)^2
E= 0.0418 Joules
Could you please help me determine if I've worked this problem out correctly.
1. Homework Statement
A 2.86-kg object on a frictionless horizontal surface oscillates at the end of a spring with an amplitude of
7.81 cm. Its maximum acceleration is 3.74 m/s2.
Calculate the total mechanical energy.
Homework Equations
1) Total Mechanical Energy: E = 0.5 k A^2
2) Spring Constant: k = m w^2 (where w = angular velocity)
3) Acceleration : a = -w^2 x
The Attempt at a Solution
Given the Amplitude A, we must calculate the spring constant k to calc the total mechanical energy.
First find w using formula 3)
w = - sqr( a / x)
w = - sqr(3.74 / 0.0781)
w = - 6.92
Now substitute k in formula 1 with formula 2 to calculate the total mechanical energy.
E = 0.5 (m w^2) A^2
E= 0.5 (2.86) (-6.92)^2 (0.0781)^2
E= 0.0418 Joules