Wow much thermal energy was generated by friction?

In summary, two parts of a problem involving a car coasting up a hill were discussed. Part (a) involved finding the height the car can coast up the hill given its initial speed and assuming negligible work done by friction. Part (b) required calculating the thermal energy generated by friction as the car actually coasted up the hill and stopped at a certain height. The solution involved using energy balance and the answer for the friction force was 247666 J.
  • #1
starJ9
3
0

Homework Statement


Suppose a car approaches a hill and has an initial speed of 116 km/h at the bottom of the hill. The driver takes her foot off of the gas pedal and allows the car to coast up the hill.

Randomized Variablesvi = 116 km/h
m = 780 kg
h = 20.5 m
a = 2.3 °

Part (a) If the car has the initial speed stated at a height of h = 0, how high (in m) can the car coast up a hill if work done by friction is negligible?

Part (b) If, in actuality, a 780-kg car with an initial speed of 116 km/h is observed to coast up a hill and stops at a height 20.5 m above its starting point, how much thermal energy was generated by friction in J?

Homework Equations


U2 + K2 = U1 + K1 + W_other
U2 is final potential energy.
K2 is final kinetic energy.

The Attempt at a Solution


Part (a) I got right.
1/2(mv^2) + mgh = 0
h = v^2/(2g)
=(32.2 m/s)^2 /(2*9.8m/s^2) = 52.9m

Part (b) I need help. (FK stands for friction force and s stands for displacement.)

I tried U2 + 0 = U1 + K1 + W_other.

W_other = -FK*s = U2 - U1 - K1
-FK*s = mg(Y2 - Y1) - 1/2(m*v^2)
-FK*s = 780kg*9.8m/s^2(20.5m*sin(2.3) - 52.9m) - 1/2(780kg*(32.2m/s)^2)
-FK*s = -652033j
FK = -(-652033j) / s
FK = 652033 j / (20.5m - 52.9m)
FK = -20124 N

The correct answer is 248200 j
 
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  • #2
What is the normal force?
What direction does the friction force act in?
Over what distance doe the friction force act?
 
  • #3
If you are familiar with conservation of energy you can get to the answer much faster..
 
  • #4
billy_joule said:
What is the normal force?
What direction does the friction force act in?
Over what distance doe the friction force act?

The normal force would be mgcos(), 780kg*9.8m/s^2*cos(2.3) = 7638N.
The friction force acts 180 degrees from the car.
I'm assuming the distance is only 20.5m.

-FK*s = mgy - 1/2(mv^2)
-FK*s = 780kg*9.8m/s^2*20.5m - 1/2(780kg*32.2^2)
-FK*s = -248430 J
FK*s = 247666 J
 
  • #5
The 20.5 m is the height above ground. You don't need to multiply by any sine or cosine when you calculate the potential energy.
You don't need normal force. Just use energy balance, as it was suggested already.
Whatever energy is "lost" is converted into heat.
 
  • #6
It seems I misread the question, the energy method is the only way to get the answer.

This threw me off:

starJ9 said:
W_other = -FK*s = U2 - U1 - K1
-FK*s = mg(Y2 - Y1) - 1/2(m*v^2)
-FK*s = 780kg*9.8m/s^2(20.5m*sin(2.3) - 52.9m) - 1/2(780kg*(32.2m/s)^2)

If μ was given you could've worked it out similar to your attempt (via W = Fd):

Wfriction = Fd
= μN * d
= μ (mg * cos (2.3) ) * (20.3m/sin(2.3))

eg heat generated equals friction force * the distance the cars odometer would read...the friction acts over a distance of greater than 500 metres. That's a lot farther than 20 metres!

starJ9 said:
-FK*s = mgy - 1/2(mv^2)
-FK*s = 780kg*9.8m/s^2*20.5m - 1/2(780kg*32.2^2)
-FK*s = -248430 J
FK*s = 247666 J

That looks correct.
 

1. How is thermal energy generated by friction?

When two objects rub against each other, the contact between them creates resistance, causing one object to slow down while the other speeds up. This resistance results in the conversion of mechanical energy into heat energy, also known as thermal energy.

2. What factors affect the amount of thermal energy generated by friction?

The amount of thermal energy generated by friction is influenced by the nature of the materials in contact, the speed of the objects, and the force applied. Additionally, the surface area of the contact and the duration of the friction also play a role in determining the amount of thermal energy produced.

3. How is the amount of thermal energy generated by friction measured?

The amount of thermal energy generated by friction is typically measured in joules (J) or calories (cal). This can be calculated by multiplying the coefficient of friction, the normal force, and the total distance traveled by the objects in contact.

4. Can friction generate more thermal energy than mechanical energy?

Yes, friction can generate more thermal energy than mechanical energy. This is because some of the mechanical energy is lost as heat due to the resistance created by friction.

5. What are the practical applications of understanding how much thermal energy is generated by friction?

Understanding the amount of thermal energy generated by friction is crucial in various fields such as engineering, physics, and materials science. It helps in designing efficient machines, reducing wear and tear of surfaces in contact, and improving the safety and performance of various mechanical systems.

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