# Will the car make it to the top of the hill?

• Dillion
In summary, a 1500 kg car traveling at 10 m/s runs out of gas while approaching an icy hill with no friction. The car will make it to the top of the hill with a final speed of 1.4 m/s. The only force acting on the car is the gravitational force, which decelerates the car. This can also be confirmed by applying Newton's second law or using conservation of energy.
Dillion

## Homework Statement

A 1500 kg car is approaching an icy (i.e. frictionless) hill as shown below. The car then runs out of gas traveling at a speed of 10 m/s. a) Will the car make it to the top of the hill?

picture is attached

## Homework Equations

vf^2 = vi^2 + 2ax[/B]

## The Attempt at a Solution

Vf is 0. Vi is 10. x is 10 (sin30 = 5/x)

0 = 0 +10a

i'm lost here at acceleration. If the car is running out of gas, how are we supposed to know how much it is slowing down by? :(

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What force causes the car to slow down?

Are you familiar with kinetic energy? and gravitational potential energy?

billy_joule said:
What force causes the car to slow down?

Are you familiar with kinetic energy? and gravitational potential energy?

1/2mvi^2 + mgh = 1/2mvf^2 + mgh

75000+73500=750vf^2+147000

vf = 1.4

as for what forces cause the car to slow down...i would say friction but this problem says frictionless.

You've found the correct speed.
You're right that there is no frictional force. What other forces are acting on the car? Can you draw a free body diagram? The relevant force is the same force that's stopping you from floating up out of your chair right now..

billy_joule said:
You've found the correct speed.
You're right that there is no frictional force. What other forces are acting on the car? Can you draw a free body diagram? The relevant force is the same force that's stopping you from floating up out of your chair right now..

Gravitational force. The gravitational force will point straight down which will be (9.8 x 1500) = 14700 N.

Dillion said:
Gravitational force. The gravitational force will point straight down which will be (9.8 x 1500) = 14700 N.
Correct. If we draw a free body diagram and define our positive x direction to be parallel to the incline and to the right then there will be some component of the gravitational force acting in the negative x direction. That is the force decelerating the car.
You could've also found the same answer you found via conservation of energy by applying Newtons second law. Though, in this case, the method you did use is faster/simpler.

## 1. Can the car make it to the top of the hill?

The answer to this question is dependent on several factors, such as the weight of the car, the slope of the hill, and the power of the car's engine. A more powerful car with a lighter weight will have a higher chance of making it to the top of the hill compared to a heavier car with a weaker engine.

## 2. How steep of a hill can a car climb?

The maximum slope a car can climb depends on the car's power, weight, and traction. Generally, a car can climb a hill with a slope of up to 30 degrees. However, this may vary depending on the car's specifications.

## 3. What is the role of traction in a car's ability to climb a hill?

Traction is crucial for a car to climb a hill successfully. It refers to the grip between the tires and the road surface. If a car has poor traction, it will have a harder time climbing a hill, especially on slippery or steep surfaces. A car with good traction, such as one with all-wheel drive, will have a better chance of making it to the top of the hill.

## 4. How does the weight of the car affect its ability to climb a hill?

The weight of a car plays a significant role in its ability to climb a hill. The heavier the car, the more power it needs to overcome gravity and climb the hill. Therefore, a lighter car will have a better chance of making it to the top of the hill compared to a heavier car with the same engine power.

## 5. What happens if a car does not make it to the top of the hill?

If a car does not make it to the top of the hill, it will either come to a stop or start rolling back down the hill. This can happen due to various reasons, such as lack of power, poor traction, or the slope of the hill being too steep for the car's capabilities. In some cases, the driver may need to reverse and try again or take an alternate route to reach the top of the hill.

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