How does the slope help in the acceleration of a car?

Question

In science, we did an experiment. The set a slop of the car at 10 degrees. We rolled down the car. then we set the slope angle at 20 degrees and this time the car accelerated faster. then we further increased the slope of the car and it accelerated faster. So why does the acceleration of the car increase as the slope is increased?

Answer 1

This is a very scientific approach to it:

The amount of gravitational potential energy will be the same, if you start it at the same height (because gravitational potential energy=height*mass and if the height and mass stay the same, then the energy is the same)

That said, the amount of potential energy that the car will turn into kinetic energy will be the same for all the trials.

It is also important to take into account that energy for anything = force * distance. The force is equal to the acceleration times the mass.

The first trial had a 10 degree slope. The length of this slope will be longer than if the slope were 20 degrees. This can be figured using right triangle trigonometry, but I think you can just trust me on that one.

If the distance is shorter for 20 degrees, and the energy stays the same, look at the equation:

energy=force*distance

Force will be more, as you need the same amount of energy with less distance. You can just input numbers to see that if you need to.

So we now have established that on the 20 degree slope, there is more force. But technically, we haven't established that there's more acceleration. So, let's go on. When force is more, and mass stays the same, we should look at the following equation:

force = mass * acceleration

We know that the car's mass did not change, but since the force went up, one of the other factors must have gone up, and if it's not the mass, then it's the acceleration. And that's why the acceleration increases when you increase the pitch of the slope

Answer 2

Set up a right triangle.

The hypotenuse is the length of the slope. The vertical leg is the height of the slope. The horizonatal leg is the length of the slope. θ is the base angle of the slope.


Draw a free body diagram. On you diagram, the object has weight which acts straight down. If you do the math, you get the following results...

N = mg cos θ

mg sin θ = ma



The important result is that last equation. Cancelling the masses, we see that a = g sin θ. Sine is an increasing function from 0 to 90º. What this means, is that as θ gets closer and closer to 90º, a gets closer and closer to g.

This makes sense as well... if the slope were at a 90º angle, then the object is in free fall and a = g.

Try it, you should always get something close to

a = g sin θ


Good luck.

Answer 3

because the car is accelerating with the force of gravity. the closer that slope comes to 90 degrees, the better. the larger the force of gravity, the faster it accelerates.

it can be explained by this equation:

Fg = ma sinx Uk (where m=mass, a=acceleration, x=angle, Uk=coefficient of kinetic friction)

Answer 4

gravity