Work Done by Spring on 0.103 kg Mass: 0.10094 J

[magma_saber]

Homework Statement

A mass of 0.103 kg hangs from a spring. you pull the mass down and has a speed 3.60 m/s. The mass moves down .10 m.
What was the work done by the earth?
When the mass moved downward, it slowed down to 2.66 m/s. What was the work done by the spring.

Homework Equations

Work done by Earth = m*g*d
Work done by spring = 1/2 m*$$\Delta$$v²?

The Attempt at a Solution

I got the work done by the Earth to be 0.10094 J.
I can't seem to get the work done by the spring. Is that the right formula? Am i suppose to take the rest energy of the spring and add that to the work done by the Earth?

 

[cse63146]

Use conservation of energy problem $$E_i = E_f$$ to determine work done by the spring.

 

[nlightner]

As a scientist, it is important to use the correct formulas and units when calculating work. The work done by the Earth can be calculated using the formula W = m*g*d, where m is the mass (0.103 kg), g is the acceleration due to gravity (9.8 m/s^2), and d is the distance the mass moved (0.10 m). Plugging in these values, we get a work done by the Earth of 0.10094 J, which is the same value provided in the problem statement.

To calculate the work done by the spring, we can use the formula W = 1/2 * k * (Deltax)^2, where k is the spring constant and Deltax is the change in position of the mass (0.10 m). The spring constant can be determined by using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. In this case, the force exerted by the spring is equal to the weight of the mass, which is given by m*g. Therefore, the spring constant can be calculated as k = m*g/Deltax = (0.103 kg)*(9.8 m/s^2)/(0.10 m) = 10.058 N/m.

Plugging in the values for k and Deltax, we get a work done by the spring of 0.013 J. This is the work done by the spring on the mass as it moves from its initial position to its final position. It is important to note that this value is independent of the speed at which the mass is moving, as the work done by a spring is determined by the displacement of the mass and the spring constant, not the velocity.

In conclusion, the work done by the Earth on the mass is 0.10094 J and the work done by the spring on the mass is 0.013 J. These values are additive, so the total work done on the mass is 0.10094 J + 0.013 J = 0.11394 J.