Force of an auto while driving

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In summary, the force felt on an auto due to its movement through still air varies approximately as the square of the car's speed. When a car is traveling at 30 miles per hour, it experiences an air resistance force of 100 pounds. Assuming the force varies exactly as the square of the speed, at 65 miles per hour, the expected air resistance force is 470 pounds. To solve this problem, we can use the equation d1/2 = v1^2/v2^2, where d1 represents the force at 100 miles per hour and v1 and v2 represent the speeds of 65 miles per hour and 30 miles per hour, respectively. By plugging in the given values and solving for
  • #1
afg_91320
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Homework Statement


The force felt on an auto due to its movement through still air varies approx. as the square of the car's speed. (the force is also known as air resistance) assume the force varies exactly as the square of the speed. around town at 30mi/hr a car experiences an air resistance force of 100lbs. what size force would you expect the car to face while traveling at 65mi/hr?

Homework Equations


car travels at 65mi/hr
at 30 mi/hr its air resistance force is 100 lbs.

The Attempt at a Solution


ive been looking at this problem for the last hour, and i don't know what good the weight will help me with. I've tried conversion but it gets me nowhere. i don't want the answer, i just want to know how should i approach the problem, and how do i start!
 
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  • #2
Welcome to PF!

afg_91320 said:
The force felt on an auto due to its movement through still air varies approx. as the square of the car's speed. (the force is also known as air resistance) assume the force varies exactly as the square of the speed. around town at 30mi/hr a car experiences an air resistance force of 100lbs. what size force would you expect the car to face while traveling at 65mi/hr?

Hi afg_91320! Welcome to PF! :smile:

This is a dimensions problem.

So write an equation with a "proportional" sign in the middle, instead of an equals sign …

Force ~ (a function of v) …

multiply v by 65/30, and what happens? :wink:
 
  • #3
ok-here is what i got:

65/30 = 100/v <-- equal sign means propotional
65v=3000
v=3000/65
v=46.153
but the answer in the back is 4.7 x 10^2 lb.
what did i do wrong?? :(
 
  • #4
Remember they said the drag was proportional to v2
 
  • #5
so that would make it:
65/30 = 100/v^2
65v^2=3000
v^2=46.153
v=6.8 <--that is incorrect.
 
  • #6
drag is prop to v2

so drag1/drag2 =v12/v22
 
  • #7
^^how does that help me?

this is what i did:
v1^2/v2^2=65/30
(100)^2/v2^2=65/30
65v^2=300,000
v^2=4615.384
but its still wrong!

can anyone show me the correct steps on how to do it! i have 3 more prblms similar to this! help me with this one, and ill be able to the others correctly!
 
  • #8
First make an estimate of the answer - so you know if your calculator got it right.
65mph is a little more than twice 30mph, so since force goes up by 4 if speed goes up by 2 we expect a force of around 400-500 lb

Now d1/2 = v1^2/v2^2
d1/100 = 65^2/30^2
d1 = 100 * (65^2/30^2) = 100 * (4225/900) = 100 * 4.69 = 470 lbs
 
  • #9
oohhh! i got it! i was just doing my math all wrong! thanks!
 

1. What is the force of an auto while driving?

The force of an auto while driving is the amount of energy or power that is required to move the vehicle forward. This force is generated by the engine and is transmitted to the wheels, which then propels the vehicle forward.

2. How is the force of an auto while driving measured?

The force of an auto while driving can be measured using a variety of methods. One common way is to use a dynamometer, which measures the power output of the engine. Another method is to measure the speed and acceleration of the vehicle and use equations such as Newton's second law of motion to calculate the force.

3. What factors affect the force of an auto while driving?

There are several factors that can affect the force of an auto while driving. These include the power and efficiency of the engine, the weight of the vehicle, the aerodynamics of the vehicle, and the road conditions. Other factors such as air resistance and friction can also play a role in determining the force of an auto while driving.

4. How does the force of an auto while driving impact fuel efficiency?

The force of an auto while driving can have a significant impact on fuel efficiency. If the force required to move the vehicle is high, it means that the engine has to work harder and consume more fuel. This is why vehicles with more powerful engines tend to have lower fuel efficiency compared to smaller and more efficient engines.

5. Can the force of an auto while driving be increased?

Yes, the force of an auto while driving can be increased by making modifications to the engine, such as increasing its power output or improving its efficiency. Other modifications, such as reducing the weight of the vehicle or improving its aerodynamics, can also help increase the force and ultimately improve the performance of the vehicle.

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