# Solving Homework Equations for Speed

• Power of One
The energy stored in the compressed spring, given by Us, is equal to the gravitational potential energy of the block, given by Ug. This means that the kinetic energy of the block at the initial point, given by KE, is equal to the energy stored in the spring. Using the equation KE=.5mv^2 and the given values, we can solve for the speed of the block when it reaches its initial point, which is approximately 0.39 m/s. Similarly, for the second question, we can use the same equation and solve for the speed of the crate at the bottom of the ramp, which is approximately 5.1 m/s. In summary, the speed of the block at its initial point is 0.39
Power of One

## Homework Statement

1. An 85 g wooden block is set up against a spring. The block is pushed into the spring, compressing it a distance of 2.0cm and then released. k= 78N/m. What is the speed of the block when it reaches its initial point.

2. A 5.0kg crate slides down a smooth ramp that is elevated at an angle of 38 degrees. length of ramp= 2m. What will be the speed of the crate at the bottom of the ramp?

Us= .5kx^2
Ug= mgh
KE=.5mv^2

## The Attempt at a Solution

1. Us= .0156J? I don't know how to find its speed.

The solution to both questions lie in the idea of conservation of energy.

To solve for the speed in these problems, we can use the equation KE = 1/2mv^2, where KE is the kinetic energy of the object, m is the mass, and v is the velocity. In the first problem, we can find the kinetic energy by first calculating the potential energy stored in the spring, which is given by Us = 1/2kx^2. Plugging in the given values, we get Us = 0.0156J. This potential energy is then converted into kinetic energy as the block is released and moves towards its initial point. So, we can set KE equal to Us and solve for v. Therefore, v = √(2Us/m) = √(2*0.0156/0.085) = 0.622 m/s. This is the speed of the block when it reaches its initial point.

For the second problem, we can use the same equation, KE = 1/2mv^2, but we first need to find the potential energy stored in the block due to its position on the ramp. This is given by Ug = mgh, where m is the mass, g is the gravitational acceleration, and h is the height of the ramp. Plugging in the given values, we get Ug = 5*9.8*2*sin(38) = 29.6J. This potential energy is then converted into kinetic energy as the block slides down the ramp. So, we can set KE equal to Ug and solve for v. Therefore, v = √(2Ug/m) = √(2*29.6/5) = 5.45 m/s. This is the speed of the crate at the bottom of the ramp.

In both of these problems, we use the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred from one form to another. We can use this principle to relate the potential energy stored in the object to its kinetic energy at different points in its motion.

## 1. How do I calculate speed in a homework equation?

To calculate speed, you need to divide the distance traveled by the time it took to travel that distance. The formula for speed is speed = distance/time. Make sure to use the same units for distance and time in your equation.

## 2. What is the difference between average speed and instantaneous speed?

Average speed is the total distance traveled divided by the total time taken, while instantaneous speed is the speed at a specific moment in time. Average speed gives an overall picture of the speed of motion, while instantaneous speed gives the speed at a specific point.

## 3. What do I do if the units in my distance and time are different?

You will need to convert the units so they are the same before calculating speed. For example, if distance is given in kilometers and time in minutes, you can convert distance to meters and time to seconds to make the units the same.

## 4. How does acceleration affect speed in a homework equation?

Acceleration is the rate of change of speed over time. It can either increase or decrease the speed depending on the direction of the acceleration. If acceleration is positive, it will increase speed, and if it is negative, it will decrease speed.

## 5. Can I use speed to determine the distance or time in a homework equation?

Yes, you can use speed to calculate distance or time, but you will need to rearrange the formula for speed. For example, to calculate distance, you can use the formula distance = speed x time, and to calculate time, you can use the formula time = distance/speed.

• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
3K
• Introductory Physics Homework Help
Replies
23
Views
9K
• Introductory Physics Homework Help
Replies
5
Views
9K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
6K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
6K