# Expressing speed with variables

• kdizzle711
In summary, the conversation discusses a problem involving a child's toy consisting of a block, spring, ball, and launching ramp. The spring has a spring constant k, the ball has a mass m, and the ramp rises a height y above the table, with the surface of the table being a height H above the floor. The problem involves calculating the speed of the ball when it leaves the ramp, and later, the speed at which it hits the floor. The conversation also mentions ignoring friction and air resistance, and suggests looking into the theory behind the problem.
kdizzle711

## Homework Statement

A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a spring constant k, the ball has a massm , and the ramp rises a height y above the table, the surface of which is a height H above the floor.

Initially, the spring rests at its equilibrium length. The spring then is compressed a distance s, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle with respect to the horizontal.

Throughout this problem, ignore friction and air resistance.

## Homework Equations

The first problem told me to calculate the speed of the ball when it leaves the launching ramp.

I got sqrt((ks^2)-2(mgy))/m
This was correct but on the next problem it is asking me with what speed will the ball hit the floor? All of this is in terms of k,s,m,g,y,or H

I have no idea where to start. My teacher does this to us every week without teaching us a thing

Well, you know m, g, and h right? That should give you a bit to get started on. You shouldn't have to concern yourself with the speed at which it comes off of the inclined plane. You might want to look at more of the theory behind the problem that just the calculations.

hope this helps somewhat

.

Hello there,

It seems like you are trying to solve a physics problem involving a child's toy and its components. Expressing speed with variables is a common practice in physics, as it allows us to generalize our equations and solve problems for different scenarios.

To start solving the problem, we need to use the equations of motion and energy conservation. We know that the potential energy of the spring is converted into kinetic energy of the ball when it is released from the launching ramp. This means that we can equate the two energies and solve for the final velocity of the ball.

Using the equation for potential energy, we have:

PE = mgy

And using the equation for kinetic energy, we have:

KE = 1/2mv^2

Since energy is conserved, we can equate these two equations and solve for the final velocity, v:

mgy = 1/2mv^2

v = sqrt(2gy)

Now, we need to find the value of y in terms of the given variables. We know that the ball is launched at an angle with respect to the horizontal, which means it follows a projectile motion. Using the equations of projectile motion, we can find the value of y:

y = H + s*sin()

Substituting this value of y in our equation for final velocity, we have:

v = sqrt(2g(H + s*sin()))

This is the final equation for the speed of the ball when it hits the floor. It is in terms of the given variables, k, s, m, g, H, and .

I hope this helps you understand how to approach this problem and solve it. It is important to remember to use the correct equations and to apply the principles of conservation of energy. Good luck with your homework!

## What is the formula for calculating speed?

The formula for calculating speed is speed = distance / time, where speed is measured in units of distance per unit of time.

## How do you express speed using variables?

Speed can be expressed using the variable s, where s = d/t, where d represents distance and t represents time.

## What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. Velocity is a vector quantity that includes both speed and direction.

## How can speed be manipulated using variables?

Speed can be manipulated using variables by rearranging the formula s = d/t. For example, if you know the distance and speed, you can rearrange the formula to solve for time: t = d/s.

## Why is it important to use variables when expressing speed?

Using variables allows for flexibility and generalization in expressing speed. It allows for the same formula to be applied to different situations and for different values to be substituted in for the variables, making calculations and comparisons easier.

• Introductory Physics Homework Help
Replies
4
Views
815
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
30
Views
768
• Introductory Physics Homework Help
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
355
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
14
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
632
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
24
Views
985