Solving a 2.1x10^3 kg Car Motion Problem

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    Car Motion
In summary, the car starts from rest at the top of a 2.1*10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20 with the horizontal. After encountering an average friction force of 4.0*10^3 N, the car reaches a speed of 3.8m/s at the bottom of the driveway. To find the length of the driveway, we must consider the net work, which takes into account both gravity and friction. By using the formula Wnet = FfdcosX and solving for the length of the driveway, we get a value of 5.1m, which differs from the book's answer due to the forgetting to
  • #1
princesspriya
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Homework Statement


a 2.1*10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20 with the horizontal. An average friction force of 4.0*10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8m/s., What is the length of the driveway?


Homework Equations





The Attempt at a Solution



Ff=4000N
2100 Kg
X=20 degrees
Vf=3.8 m/s
Vi=0 m/s

Wnet=1/2MVf^2-1/2MVi^2
Wnet= 1/2*2000*3.8^2
Wnet= 15162 N

Wnet = FfdcosX
15162=4000cos20D
D=4.03m

but the book says 5.1m?
i can't figure out what i did wrong
thx for the help.
 
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  • #2
You forgot about gravity. Friction just slows the car; it's gravity which pulls it down the slope.

To find the net work you must consider all the forces: gravity and friction. (Don't forget that they act in different directions.)
 
  • #3
i see so the force applied would be Fgravity*sin20 which would give me 7045.96 and i would subtract the Ff to get the total force. right?
 
Last edited:
  • #4
princesspriya said:
i see so the force applied would be Fgravity*sin20 which would give me 7045.96 and i would subtract the Ff to get the total force. right?
Right!
 
  • #5
thxxx
 

1. How do you calculate the acceleration of a car?

To calculate the acceleration of a car, you need to know the mass of the car and the net force acting on it. You can use the equation a = F/m, where a is the acceleration, F is the net force, and m is the mass of the car.

2. What is the net force acting on a car?

The net force acting on a car is the sum of all the forces acting on it. This includes the force of friction, air resistance, and the force provided by the car's engine. It can be calculated by using the equation F = ma, where F is the net force, m is the mass of the car, and a is the acceleration.

3. How do you solve a 2.1x10^3 kg car motion problem?

To solve a 2.1x10^3 kg car motion problem, you need to first identify the given information, such as the mass of the car, the net force acting on it, and the acceleration. Then, you can use the equations a = F/m and v = u + at to calculate the final velocity of the car.

4. What is the final velocity of a 2.1x10^3 kg car with an acceleration of 5 m/s^2?

The final velocity of a 2.1x10^3 kg car with an acceleration of 5 m/s^2 can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity (usually assumed to be 0 for a stopped car), a is the acceleration, and t is the time elapsed. This will give you the final velocity in m/s.

5. How do you convert the final velocity of a car from m/s to km/h?

To convert the final velocity of a car from m/s to km/h, you can use the conversion factor 3.6. Simply multiply the final velocity in m/s by 3.6 to get the final velocity in km/h. For example, if the final velocity is 30 m/s, then the final velocity in km/h would be 30 x 3.6 = 108 km/h.

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