Calculate speed (work and energy)

In summary, the problem involves a compressed vertical spring with a spring constant of 300 N/m and a 0.25 kg ball placed on top. When released, the ball flies vertically upward and the question is asking for its speed when it has reached a height of 0.1 m. By using the conservation of energy, the maximum height of the ball can be calculated to be 0.22 m. However, the solution could have been simplified by only considering the spring potential energy. The final velocity is calculated to be 1.53 m/s. The only ambiguity in the problem lies in the measurement of the height, as it is not specified from which position it should be measured.
  • #1
moved from general physics
A vertical spring with spring constant 300 N/m is compressed 0.06 m and a 0.25 kg ball placed on top. The spring is released and the ball flies vertically upward.

What is the ball's speed when it has gone 0.1 m high?

I don't know which relationship is required to find the speed, Can someone please help?
I calculated the maximum hight:
mgh = 1/2Dy^2
h = 0.22 m

Then i made use of the formula
E(final) = E(Initial)

0.25 * g * 0.22 = 0.25 * g * 0.1 + 1/2 * 0.25 * v^2
v = 1.53m/s

Is that correct?
 
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  • #2
Not sure why you went to the trouble of using the maximum height. All you really need is the total energy at any instant, so the spring potential energy alone would suffice if you take the zero-reference for gravitational PE to be the ball's pre-release position.

The only really questionable part of your solution is the vagueness of "0.1 m high" in the problem statement. Where's the height measured from? Is it the position of the ball before the spring is compressed, or the position of the ball when the spring is compressed?
 
  • #3
I don't know which relationship is required to find the speed...

Conservation of energy. The ball starts off with an initial KE that is converted into a combination of PE and KE on the way up. You can calculate the PE at any height (eg at 0.1M). The remaining energy is KE from which you calculate the velocity.
 

1. What is the formula for calculating speed using work and energy?

The formula for calculating speed using work and energy is speed = work/energy.

2. Can you explain the concept of work and energy in relation to speed?

Work is the amount of force applied over a distance, while energy is the ability to do work. In order for an object to move at a certain speed, work must be done to overcome the object's inertia and energy is needed to sustain that speed.

3. Is speed the only factor affected by work and energy?

No, work and energy also affect an object's kinetic and potential energy. Kinetic energy is the energy an object has due to its motion, while potential energy is the energy an object has due to its position or state. Work and energy can change an object's speed, kinetic energy, and potential energy.

4. What units should be used when calculating speed using work and energy?

The units used for speed are typically meters per second (m/s) or kilometers per hour (km/h). However, the units used for work and energy can vary depending on the type of system being analyzed. Some common units include joules (J), calories (cal), or foot-pounds (ft-lb).

5. How does friction affect the calculation of speed using work and energy?

Friction is a force that opposes the motion of an object. In order to maintain a constant speed, an object must overcome the force of friction. This means that more work and energy will be required to maintain the same speed in the presence of friction. Therefore, friction will affect the calculation of speed using work and energy.

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