# Finding Speed to Push Cart up Hill

• ReoFonzo
In summary, the boy needs to push the cart at a speed of 2 meters per second in order to just make it to the brother on the bed.
ReoFonzo

## Homework Statement

I have to find the speed needed to push a cart on top of a hill and I only have the height as a number.

## Homework Equations

A boy places his matchbox car at the top of the track he has set up with his brother. If the track starts atop the 55 cm toy box, descends to the floor and then up to the 75cm high bed where his brother waits for the car. How fast must the boy push his cart so it just makes it to the brother on the bed ?

## The Attempt at a Solution

PE = m(10m/s).55m = 55JM ?

You have nothing about speed in your attempted solution. Where do you think it applies?

I have an awnser sheet and it says 2m/s... I'm supposed to find what force pushed the cart above the second hill which I assume is kinetic energy but I have no mass which I don't understand...

ReoFonzo said:
I have an awnser sheet and it says 2m/s... I'm supposed to find what force pushed the cart above the second hill which I assume is kinetic energy but I have no mass which I don't understand...

Kinetic energy is involved in the problem. The initial speed gives the car initial kinetic energy. During the motion some energy is transformed fom potential to kinetic and then the kinetic is transformed to potential.

The mass is a factor in both the kinetic and potential energies. Its value does not matter. Do the problem with the mass represented by M. In the end you will find the initial speed required is the same for any mass of the car.

Last edited:
ReoFonzo said:
I have an awnser sheet and it says 2m/s... I'm supposed to find what force pushed the cart above the second hill which I assume is kinetic energy but I have no mass which I don't understand...

One trick of simple math problems is to immediately start filling things in and use arbitrary numbers if needed, as long as that variable is a part of every term in the equation. This method is particularly useful for ratios between things, where factoring can get complicated. Making up numbers only works if you can look at the equation and think "this can be factored, but i don't feel like doing that."

For the problem given it's as simple as finding the energy difference between where the car starts and where it finishes, which is a difference of 20cm.
(m)(g)(h) = (1/2)(m)(v^2)
m can be factored out, g is gravity (9.something), h is 20cm (convert it to meters)
Solve for v.

Thanks a lot guys!

## 1. What is the formula for calculating speed?

The formula for calculating speed is speed = distance / time.

## 2. How does the weight of the cart affect its speed?

The weight of the cart affects its speed by increasing the force required to move it and therefore decreasing its overall speed.

## 3. Does the incline of the hill affect the speed of the cart?

Yes, the incline of the hill affects the speed of the cart. The steeper the incline, the more force is required to push the cart up the hill, resulting in a slower speed.

## 4. How does friction play a role in determining the speed of the cart?

Friction plays a significant role in determining the speed of the cart. The level of friction between the wheels of the cart and the surface of the hill can significantly impact the speed at which the cart can be pushed up the hill.

## 5. Is there a limit to how fast a cart can be pushed up a hill?

Yes, there is a limit to how fast a cart can be pushed up a hill. This limit is determined by factors such as the weight of the cart, the incline of the hill, and the level of friction present. Additionally, the strength and force exerted by the person pushing the cart also play a role in determining the maximum speed that can be achieved.

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