(a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible

and its initial speed is 110 km/h? (b) If, in actuality, a 750-kg car with an initial speed of 110 km/h
is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy
was generated by friction? (c) What is the average force of friction if the hill has a slope 2.5°
above the horizontal?

110 km/hr = 110,000 m/3600 s = 30.6 m/s

m g h = (1/2) m v^2

9.81 h = .5 (30.6)^2

h = 47.7 meters

(b) loss of energy = m g (47.7-22)
= 750(9.81)(25.7) = 189,000 Joules lost

(c) work done = force in direction of motion * distance moved

189,000 = F (22/sin2.5)

F = 375 N

Thank You

You are welcome.

I disagree with the answer to (c). The distance traveled (d) is not the same as the height the car has reached at the end of its coasting. d is actually the hypotenuse. so h=dsin(2.5) thus d=h/sin(2.5), so d=22/0.424 which is 52.1, the distance traveled. Plugging this into the work done by friction,(Wf), Wf= Fdcos(2.5), F= Wf / dcos(2.5),F = 189,000/52.06cos2.5 = 3634N.

Hi, your response to question c) is right but for the wrong reasons and could be easily misconstrued as the correct method. Taking the value of energy loss from the previous question as the work done by friction we can use the equation for work with respect to the force, displacement and angle at which the force is applied. The displacement is in fact the hypotenuse, as is given by (22/sin(2.5 degrees)). The primary mistake however is ignoring the fact that the force of friction is acting in the opposite direction of the car, and therefore the angle that should be used in the work equation is 180 degrees, not the 2.5 as some others have suggested. This gives the value of F to be -375N, which when looking solely for the magnitude gives the force of friction to be 375N.

(a) Well, as a car enthusiast, I can tell you that coasting up a hill in a car with the engine disengaged can be a real uphill battle. Pun intended. But let's crunch some numbers.

To find out how high a hill the car can coast up, we need to consider kinetic energy and potential energy. The initial kinetic energy of the car is converted into potential energy as it climbs the hill.

Using the principle of conservation of energy, we can equate the initial kinetic energy to the final potential energy:

1/2 * m * v^2 = m * g * h

Here, m represents the mass of the car, v is the initial speed, g is the acceleration due to gravity, and h is the height of the hill.

Now, let's plug in the given values:

m = mass of car = ? (not given)
v = initial speed = 110 km/h = ? (converting units)
g = acceleration due to gravity = 9.8 m/s^2
h = height of hill = ? (to be found)

Hmm, it seems like we're missing some values here. Without the mass of the car, it's impossible to determine the height of the hill. So, let's move on to the next question!

(b) Oops, looks like we still don't have the mass of the car. Without that information, I can't calculate the thermal energy generated by friction. It seems like someone forgot to give us the complete picture here. Time to put on my detective nose and find the missing piece of this puzzle!

(c) Ah, the slope of the hill! This question seems to be playing hide and seek with information. We're missing the coefficient of friction and the mass of the car, which are both needed to calculate the force of friction.

Well, it seems like this hill has more mysteries than a detective novel. If only we had all the necessary information, we could solve these problems. But for now, let's leave the case open and move on to another question, shall we?

To solve these questions, we need to use the concepts of work, energy, and friction.

(a) To determine how high a hill a car can coast up, we can use the conservation of mechanical energy. The initial kinetic energy of the car will be transformed into potential energy as it climbs the hill. Assuming negligible work done by friction, the total mechanical energy of the car is conserved.

The potential energy of an object is given by the equation:
PE = mgh,

where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the hill.

The initial kinetic energy of the car is given by the equation:
KE = (1/2)mv^2,

where m is the mass of the car and v is the initial velocity of the car.

Setting the potential energy equal to the initial kinetic energy and solving for h, we have:
mgh = (1/2)mv^2,
h = (1/2)v^2/g.

Inserting the given values, we can calculate the height of the hill.

(b) To determine the thermal energy generated by friction, we need to calculate the work done by friction. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by friction is converted into thermal energy.

The work done by friction is given by the equation:
W = ΔKE + ΔPE,

where ΔKE is the change in kinetic energy and ΔPE is the change in potential energy.

In this case, the change in kinetic energy is zero because the car starts and stops at the same speed. Therefore, the work done by friction is equal to the change in potential energy:
W = ΔPE = mgh.

Using the given values of mass, height, and acceleration due to gravity, we can calculate the thermal energy generated by friction.

(c) To determine the average force of friction, we need to use the equation for the gravitational force and the slope of the hill.

The gravitational force acting on the car is given by:
F = mg,

where m is the mass of the car and g is the acceleration due to gravity.

The force of friction acting on the car is opposite to the motion and can be represented as:
Ff = μmg,

where μ is the coefficient of friction.

Since the hill has a slope, the force of friction can be decomposed into two components: the normal force and the force parallel to the slope. The normal force is given by:
Fn = mg cos(θ),

where θ is the angle of the slope.

The force parallel to the slope is given by:
Ff = mg sin(θ).

Using the given slope angle, we can calculate the average force of friction.

Remember to always double-check your calculations and use appropriate units throughout your calculations.