How to Calculate Speed of a Car Rolling Down a Hill

In summary: There are three forces acting on it: the force of gravity, the force of the floor, and the force of the incline. The equation of motion is: m(x,t)=-gx+kx^2+fy (where m is the mass of the object, x is the distance down the slope, t is time, and y is the height above the floor). Notice that the acceleration is simply a change in velocity: v(x,t)=-gvx+kv^2+fy. Also, note that the acceleration is always downwards (the incline increases the velocity downwards).
  • #1
tommy-d
2
0
Hi there currently I am stuck on a question, A car with a mass of 1.2 tonnes, rolls down a hill which is 600m long and is inclined at an angle of 9 degrees to the horizontal. Ignoring the effects of air resistance and friction and assuming the car to start from rest at the top of the hill calculate:

Its speed as it reaches the bottom of the hill.

Its acceleration down the hill

The time taken for it to reach the bottom of the hill.

The part that I am having the difficulty with is the speed as it reaches the bottom of the hill, I've looked over and over and can't find anything on it. does anyone know a formula for this? or a way to calculate it?

Many thanks Tom
 
Physics news on Phys.org
  • #2
Welcome to PF!

Velocity changes due to acceleration. What causes the acceleration?

How is acceleration related to some of the given info? Have you studied Newton's laws?

Can you write a velocity equation for this motion?

Please, show your work. Don't be afraid to post wrong answers. It's better if a student submits two pages of nonsense than a blank page.
 
  • #3
the only formula i can get close to for this is ax = T/m- g sin9° i have written this out to be 0/1200-9.81sin(9) = -1.53. this would mean that the speed when the car would be exiting the ramp would be 1.53 m/s but I'm not confident on this answer as it doesn't mention the length of the ramp in the formula. any suggestions?

Many thanks tom
 
  • #4
Can you show me your work? How did you derive this formula?

Try drawing a diagram. Then draw the x-axis (or call it a bob-axis, it doesn't really matter) in the direction of motion. Write down all the forces acting on this car. How is a force connected with acceleration? What is the general equation of motion?

Remember that this case can be simplified to the inclined plane problem (we don't care if it's either Ferrari or an old Volvo). An object with a constant coefficient of friction is sliding down the plane.
 

1. How does the mass of the car affect its speed while rolling down a hill?

The mass of the car does not directly affect its speed while rolling down a hill. However, it does affect the car's potential energy, which can then be converted into kinetic energy as it moves downhill. Therefore, a heavier car may have more potential energy and may reach a higher speed than a lighter car.

2. How does the steepness of the hill impact the car's speed?

The steeper the hill, the greater the force of gravity acting on the car. This results in a higher acceleration and therefore a higher speed. However, if the hill is too steep, the car may reach a point where it cannot gain any more speed due to friction and air resistance counteracting the force of gravity.

3. What role does friction play in the movement of the car down the hill?

Friction acts as a resistance force on the car, slowing it down as it moves down the hill. The type of surface the car is rolling on, as well as the weight and shape of the car, can affect the amount of friction present. This is why smoother surfaces and lighter, more aerodynamic cars can roll down a hill faster than rougher surfaces and heavier, less streamlined cars.

4. How does the shape of the car impact its movement down the hill?

The shape of the car can affect its speed while rolling down a hill. A more streamlined and aerodynamic shape will experience less air resistance, allowing it to maintain a higher speed. On the other hand, a boxy or bulky shape will experience more air resistance and may slow down more quickly.

5. Can the car continue rolling indefinitely down a hill?

In theory, yes, the car can continue rolling down a hill indefinitely if there is no external force acting on it. However, in reality, friction and air resistance will eventually slow the car down to a stop. Additionally, if the hill is not steep enough, the car may not have enough potential energy to continue rolling.

Similar threads

A cylinder of snow rolls down a hill gathering more snow -- calculate its speed
    • Introductory Physics Homework Help
2
Replies
39
Views
2K
Automotive Speed of a car rolling down a hill
    • Mechanical Engineering
2
Replies
44
Views
5K
Why Does a Car Accelerate When Rolling Down a Hill?
    • Introductory Physics Homework Help
Replies
11
Views
2K
Final velocity of a car rolling down a ramp using energy
    • Introductory Physics Homework Help
Replies
1
Views
3K
Maximum speed of car on downhill
    • Introductory Physics Homework Help
Replies
1
Views
1K
Help Me Hill Height for 35kg Child on 5kg Sled
    • Introductory Physics Homework Help
Replies
6
Views
812
How to calculate the kinematics of an object pushed up an inclinex plane?
    • Introductory Physics Homework Help
Replies
7
Views
874
Car on a hill - reasoning for static friction
    • Introductory Physics Homework Help
Replies
5
Views
5K
Sphere Rolling Down Hill into Projectile Motion
    • Introductory Physics Homework Help
Replies
3
Views
2K
Minimum safe height for a roller coaster
    • Introductory Physics Homework Help
Replies
10
Views
4K

Hot Threads

Recent Insights

Back
Top