# Energy/ work problem set(last question )

• Moe*
In summary, the question involves a 53.5 g ice cube sliding up and down a 33.0° slope with a spring at the bottom that is compressed 12.0 cm. The spring constant is 22.0 N/m. Using the equations for potential energy of the spring and potential energy due to gravity, we can calculate the total distance the ice cube will travel up the slope, which is equal to 1.02m + 0.12m (compression of spring). However, it is important to note that while calculating the potential energy due to gravity, the component of g should not be taken into account.
Moe*
Energy/ work problem set(last question!)

## Homework Statement

A 53.5 g ice cube can slide without friction up and down a 33.0° slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 12.0 cm. The spring constant is 22.0 N/m. When the ice cube is released, what total distance will it travel up the slope, from the time the spring is fully compressed until reversing direction?

## Homework Equations

1/2kx^2, mgh, maybe 1/2mv^2

## The Attempt at a Solution

here's my best shot:
PE(spring) at bottom=PE(grav) at top
1/2kx^2 = mgh
since gravity has a component in x direction:
1/2kx^2 = mhgsin33
since sin33=h/d, h=dsin33:
1/2kx^2=m(dsin33)(gsin33)

using this, i got 1.02m+.12m (compression of spring).
i tried with and without compression of the spring, stillc ouldn't get the right ans. I'm sure 1 m is too long for a titchy little icecube to travel. any help would be appreciated.

1/2kx^2=m(dsin33)(gsin33)

While calculating the PE due to gravity you should not take the component of g.
So 1/2*k*x^2= mgdsin 33

thank you... and sorry about the long response

## 1. How do I calculate the work done by a force on an object?

The work done by a force on an object is equal to the magnitude of the force multiplied by the distance the object moves in the direction of the force. This can be expressed as W = Fd, where W is work, F is force, and d is distance.

## 2. What is the difference between kinetic and potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state. Kinetic energy can be calculated as KE = 1/2mv^2, where m is mass and v is velocity. Potential energy can be calculated as PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height.

## 3. How does friction affect the amount of work done?

Friction is a force that opposes motion, so it reduces the amount of work done by a force. This means that the work done by a force on an object will be less than the force multiplied by the distance it moves due to the presence of friction.

## 4. Can you have negative work?

Yes, work can be negative. This occurs when the force and the displacement are in opposite directions, meaning the work being done is against the motion of the object. For example, if a person pushes a box up a ramp and the box slides back down, the work done by the person would be negative.

## 5. How can I calculate the power of a system?

Power is the rate at which work is done, so it can be calculated by dividing the work done by the time it takes to do the work. This can be expressed as P = W/t, where P is power, W is work, and t is time. Power can also be calculated by multiplying force and velocity, as power is equal to force times velocity.

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