Elastic potential energy - springs

In summary, the problem involves a 2.00-kg block being pushed against a spring with a force constant of 400 N/m, compressing it 0.220 m. When released, the block moves along a frictionless horizontal surface and then up a frictionless incline with a slope of 37 degrees. The question is asking for the speed of the block after it leaves the spring. To solve this, the equation K1 + U2 = K2 + U2 is used, where K represents kinetic energy and U represents potential energy. Since the block is not initially moving and is not compressing the spring when it leaves, K1 and U2 are both 0. K2 represents the kinetic energy of the
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I know this problem has been asked before but i am trying to understand.

Homework Statement



A 2.00-kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with slope 37 degrees

(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?

Homework Equations



K1 + U2 = K2 + U2
Vel = 1/2 kx^2

K = 1/2mv^2

The Attempt at a Solution



If i think of K1 and U1 as the spring compressed then K2 + U2 is the box leaving the spring.
If that logic is correct.?

My teacher has taught us to do this:

K1 =
U1 =
K2 =
U2 =

Now, i am confused on how to fill it in. Then, i can use K1 + U2 = K2 + U2.
can you help me fill in and explain why? I think this will help me understand how to do the problem.

In my mind potential energy is converted to kinetic energy? So, saying K1 + U2 is spring compressed
K1 = 0
U1 = 1/2 kx^2
K2 = 1/2 mv^2
U2 = 0
 
Last edited:
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  • #2
You've done it right.
The box isn't moving initially, so the kinetic energy is 0.
The box isn't compressing the spring when it leaves, so the potential energy is 0.
 

Related to Elastic potential energy - springs

1. What is elastic potential energy?

Elastic potential energy is a type of potential energy stored in an object when it is stretched or compressed by a force. It is a result of the object's ability to return to its original shape after the force is removed.

2. How do we calculate elastic potential energy?

The formula for elastic potential energy is E = 1/2kx^2, where E is the energy in joules, k is the spring constant in N/m, and x is the displacement in meters. This formula assumes that the spring obeys Hooke's Law.

3. What is Hooke's Law?

Hooke's Law states that the force applied to an elastic object is directly proportional to the amount of stretch or compression of the object. This means that the spring constant, k, is a constant value for a specific spring and the amount of force applied to it.

4. How does the stiffness of a spring affect its elastic potential energy?

The stiffness, or spring constant, of a spring directly affects its elastic potential energy. A stiffer spring will require more force to stretch or compress, resulting in a higher potential energy. A less stiff spring will require less force and have a lower potential energy.

5. Can elastic potential energy be converted into other forms of energy?

Yes, elastic potential energy can be converted into other forms of energy, such as kinetic energy. When the object is released from its stretched or compressed state, the potential energy is converted into motion energy as the object returns to its original shape.

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