Running Out of Gas - work & power problem

In summary, the problem involves a car rolling down a 150 m hill at a speed of 36 km/h before running out of gas. The road down the hill is 3000 m long and the car continues to roll on a horizontal section of road. The car and driver have a mass of 1000 kg and the rolling friction is 400 N. Neglecting air drag and using g = 10 m/s2, the problem asks for the final speed (vf) at the bottom of the hill when the brakes are not applied. After attempting to solve using various equations, the correct solution is 10 m/s, which is an overestimate due to neglecting air drag.
  • #1
DraculaNotI
2
0
1. Homework Statement :
You are at the top of a hill that is 150 m in height and are traveling at 36 km/h when your car runs out of gas. Due to the relatively shallow grade, the road down the hill is 3000 m long. After rolling down the hill, the car continues to roll on a horizontal section of road. The mass of the car and driver is 1000 kg and on both the hill and the horizontal stretch, the rolling friction is equal to 400 N. Neglect air drag in this problem and use g = 10 m/s2.


2. Homework Equations :
Assuming you do not apply the brakes, what is your speed vf when you arrive at the bottom of the hill? Remember that this answer will be an overestimate since we are neglecting air drag.
Give your answer to 3 significant figures in km/h. Pay careful attention to your signs in this question!


3. The Attempt at a Solution :
I've tried been using these equations that we went over in class...
Kf - Ki = -f*d (not sure if this is relevant)
Wfriction = [tex]\Delta[/tex]U + Kf - Ki
Converting vi to m/s: 36*1000/3600 = 1
(400*3000) = 1,500,000 + (1/2)(1000)*vf2 - (1/2)(1000)(1)
...which ends up in a disaster of imaginary numberness if I'm punching it all in correctly. D:
I've also tried some other methods (putting minus signs wherever), but my answers (I've gotten 176m/s and 88.3m/s) have come up as wrong every time.

Any help would be greatly appreciated! :)
 
Physics news on Phys.org
  • #2
DraculaNotI said:
Wfriction = [tex]\Delta[/tex]U + Kf - Ki

Converting vi to m/s: 36*1000/3600 = 1
(400*3000) = 1,500,000 + (1/2)(1000)*vf2 - (1/2)(1000)(1)
...which ends up in a disaster of imaginary numberness if I'm punching it all in correctly. D:

36*1000/3600 = 10, not 1

The work done by friction is always negative, and so is [itex] \Delta U [/itex] because the
car has less gravitational potential energy when it has moves down the hill.
 
  • #3
Thank you, willem2! It makes a lot more sense now (plus I've had a good 9 hours of sleep). :)

Lesson learned: don't try to convert units in your head at 1am
 

FAQ: Running Out of Gas - work & power problem

1. How can I calculate the work done by a car running out of gas?

To calculate the work done by a car running out of gas, you will need to know the distance traveled and the force required to move the car. The equation for work is W = F x d, where W is work, F is force, and d is distance. The force required to move the car can be calculated using the equation F = m x a, where m is the mass of the car and a is the acceleration. Once you have calculated the force and distance, you can plug them into the work equation to find the work done by the car.

2. What is the relationship between work and power in this scenario?

Work and power are closely related in this scenario. Power is the rate at which work is done, and it is calculated by dividing work by time. The less time it takes for the car to run out of gas, the higher the power output. In other words, the faster the car is traveling, the more power it is using to move.

3. Can you explain the concept of energy conversion in this problem?

In this problem, energy is being converted from the chemical energy in the gasoline to kinetic energy, which is the energy of motion. When the gasoline is burned in the engine, it releases energy that is used to power the car and move it forward. As the car runs out of gas, the energy conversion stops, and the car slows down and eventually stops.

4. How does the weight of the car affect its ability to move when it runs out of gas?

The weight of the car plays a significant role in its ability to move when it runs out of gas. The heavier the car, the more force is required to move it. This means that a heavier car will use more energy and run out of gas faster than a lighter car. Additionally, the weight of the car will also affect the power output, as a heavier car will require more power to move.

5. Are there any other factors that can affect the work and power of a car running out of gas?

Yes, there are other factors that can affect the work and power of a car running out of gas. These include the engine efficiency, road conditions, and air resistance. A more efficient engine will use less energy and require less work to move the car, while poor road conditions or high air resistance will require more work and power to keep the car moving. Additionally, the weight of the cargo and passengers in the car can also affect its work and power output.

Back
Top