Conversation of mechanical energy

In summary, a 700 g block released from rest at height h(not) above a vertical spring with spring constant k=400 N/m and negligible mass compresses the spring by 19.0 cm before stopping. The work done by the block on the spring is 7.22J and the work done by the spring on the block is -7.22J. The value of h(not) is 0.86 m. If the block were released from a height of 2.00h(not), the maximum compression of the spring would be 0.26 m.
  • #1
gujubomber
1
0

Homework Statement


A 700 g block is released from rest at height h(not) above a vertical spring with spring constant k= 400 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 19.0 cm. How much work is done (a) by the block on the spring and (b) by the spring on the block? (c) What is the value of h(not)? (d) If the block were released from height 2.00h(not) above the spring, what would be the maximum compression of the spring?


Homework Equations


h(not)=h0

Work on block wb= -1/2 kx^2
h(not)=-x +1/2 kx^2/mg
to find x :kx^2 -2mgx - 4mgh(not) = 0



The Attempt at a Solution


a. i used work on block and got 7.22J
b. would be opposit energy of work on block thus being -7.22J
c.used h(not) and got 0.86 m
then from finding x i used quadratic formul and got x=0.26 m
d. do not know how to find2.00h(not)
 
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  • #2
You seem to have answered problem d at the end of problem c. I think you need
3 significant digits in your answer.
 

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

The law of conservation of mechanical energy states that the total amount of mechanical energy (the sum of kinetic and potential energy) in a closed system remains constant over time. This means that energy cannot be created or destroyed, it can only be transferred or transformed from one form to another.

2. Why is the conservation of mechanical energy important?

The conservation of mechanical energy is important because it is a fundamental law of physics that helps us understand and predict the behavior of objects and systems. It allows us to analyze and solve problems involving energy in various forms, such as motion, forces, and work.

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

In real-world situations, mechanical energy is conserved through various processes such as friction and energy transfer. For example, when a ball is thrown into the air, its kinetic energy decreases as it reaches the highest point of its trajectory, but its potential energy increases. When the ball falls back to the ground, its potential energy decreases and its kinetic energy increases back to its original value. In this way, the total mechanical energy remains constant.

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

Yes, according to the law of conservation of energy, mechanical energy can be converted into other forms of energy, such as thermal energy or electromagnetic energy. For example, when a car's brakes are applied, the kinetic energy of the moving car is converted into thermal energy due to friction between the brake pads and the wheels.

5. Is the conservation of mechanical energy always applicable?

No, the conservation of mechanical energy is not always applicable in all situations. It is only valid in closed systems, where there is no external work or energy transfer. In real-world scenarios, there can be external forces or factors that can affect the total mechanical energy of a system, such as air resistance or non-conservative forces like friction.

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