Solving an 1100kg Car's Work Output on a 50m Hill

In summary, the conversation discusses the calculation of work produced by the engine of a car that starts at rest at sea level and climbs a hill, reaching a speed of 25 m/s at the top. The equation W = F(d) is used, along with the equation F = ma, to solve for the work produced. It is determined that there are two components of work, one for overcoming potential energy and one for the car's final velocity, and these are added together to get the total work produced. The final answer is 882,750 J.
  • #1
PhilCam
46
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Homework Statement



A car of mass 1100kg starts from rest at sea level and climbs a hill of altitude of 50 m. At the top of the hill the car has a speed of 25 m/s.

The work produced by the engine of the car is?


Homework Equations


W= F(d)
F= ma

The Attempt at a Solution


W = Force x 50m
Yea, I have tried this problem about 8 different ways, but it says the correct answer is 882,750 J and I cannot figure out how to get that from the numbers given.

Any help would be great, thanks.
 
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  • #2
PhilCam said:

Homework Statement



A car of mass 1100kg starts from rest at sea level and climbs a hill of altitude of 50 m. At the top of the hill the car has a speed of 25 m/s.

The work produced by the engine of the car is?


Homework Equations


W= F(d)
F= ma

The Attempt at a Solution


W = Force x 50m
Yea, I have tried this problem about 8 different ways, but it says the correct answer is 882,750 J and I cannot figure out how to get that from the numbers given.

Any help would be great, thanks.

There are two different things here that require work for the engine:

W = W1 + W2

One of them is the potential energy overcome by climbing the hill, W1. This would be enough if the object came to rest at the top of the hill, but it's didn't. It still has a velocity. From this, you might be able to guess what W2 is.
 
  • #3
Thank you very much, I got it.
 

FAQ: Solving an 1100kg Car's Work Output on a 50m Hill

How do you calculate the work output of an 1100kg car on a 50m hill?

In order to calculate the work output, you will need to use the following formula: Work = Force x Distance. First, you will need to calculate the force exerted by the car, which can be found by multiplying the mass of the car (1100kg) by the acceleration due to gravity (9.8 m/s^2). This will give you the force in Newtons (N). Next, you will multiply the force by the distance the car travels up the hill (50m) to get the work output in Joules (J).

What is the significance of calculating a car's work output on a hill?

Calculating a car's work output on a hill can provide valuable information about the car's performance and efficiency. It can also help in determining the amount of energy required to move the car up the hill, which can be useful for designing more efficient and environmentally-friendly vehicles.

Is the work output of a car on a hill affected by its speed?

Yes, the speed of the car can affect the work output. The faster the car is moving, the more kinetic energy it has, and therefore, the more work it can do on the hill. However, other factors such as the car's engine power and weight also play a significant role in determining the work output.

Can the work output of a car on a hill be negative?

Yes, the work output of a car on a hill can be negative. This can happen if the car is moving downhill and is using its brakes to slow down. In this case, the car is actually expending energy (through the brakes) rather than performing work on the hill, resulting in a negative work output.

How can the work output of a car on a hill be useful in real-life applications?

The work output of a car on a hill can be useful in a variety of real-life applications. For example, it can be used to determine the amount of energy required to climb a steep hill, which can be useful for planning road trips or designing transportation routes. It can also be used to evaluate the efficiency of different car models and how they perform on hills.

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