Conservation of Mechanical energy

• mia_material_x1
In summary, the conversation discusses an 8.00 kg stone at rest on a compressed spring, determining the spring constant and elastic potential energy of the spring before release. The question also asks for the change in gravitational potential energy and maximum height of the stone. The solution involves using equations for force, work, and mechanical energy conservation to find the answers.

Homework Statement

Attached figrue shows an 8.00 kg stone at rest on a spring.The spring is compressed 10.0 cm by the stone.
(a) What is the spring constant?
(b) The stone is pushed down an additional 30.0 cm and released.What is the elastic potential energy of the compressed spring just before that release?
(c) What is the change in the gravitational potential energy of the stone–Earth system when the stone moves from the release point to its maximum height?
(d) What is that maximum height, measured from the release point?

F = mg
F = -kx
W = 1/2 (kx²)

The Attempt at a Solution

m = 8kg
x1 = - 0.1m
x2= - 0.1m - 0.3m = -0.4m

Don't worry about a) and b), I've worked them out here just in case of reference
a) F=mg=-kx1 ⇒k=784 n/m
b) kΔx²/2= (784 n/m)(-0.1m-0.3m)²/2 = 62.72 J

What I have trouble with is c), can someone explain how I should deal with this question? (p.s, You are awesomeee if you can accompany your explanation with drawing) http://imgur.com/t4BkCe1

Much thanks!

mia_material_x1 said:
What I have trouble with is c), can someone explain how I should deal with this question?
The title of your thread is a big hint! Mechanical energy is conserved. At the lowest point, what is the total mechanical energy? (Measure gravitational PE from that point.) At the highest point?

1. What is the law of conservation of mechanical energy?

The law of conservation of mechanical energy states that in a closed system, the total amount of mechanical energy (potential energy + kinetic energy) remains constant. This means that energy can neither be created nor destroyed, but it can only be transferred or transformed from one form to another.

2. How is mechanical energy conserved in real-world situations?

In real-world situations, mechanical energy can be conserved through various processes such as frictionless motion, elastic collisions, and energy transfer between different forms (e.g. potential to kinetic). However, in most cases, some amount of mechanical energy is lost due to factors like friction, air resistance, and other external forces.

3. What is the significance of conservation of mechanical energy?

The conservation of mechanical energy is a fundamental law of physics that has many practical applications. It helps us understand and predict the behavior of objects in motion, such as the trajectory of a projectile or the motion of a pendulum. It also allows us to design efficient machines and devices by minimizing energy loss.

4. Can mechanical energy be converted into other forms of energy?

Yes, mechanical energy can be converted into other forms of energy, such as thermal energy or electrical energy. For example, when a moving object comes to a stop due to friction, its kinetic energy is converted into thermal energy, causing the object and its surroundings to heat up.

5. Is the conservation of mechanical energy applicable to all systems?

No, the conservation of mechanical energy is only applicable to closed systems where no external forces are acting. In open systems, where there is an exchange of energy with the surroundings, the total mechanical energy may not remain constant. For example, a car moving on a road is an open system as it experiences external forces like friction and air resistance, causing a decrease in its mechanical energy over time.