Calculation of gradient resistance / Berechnung des Steigungswiderstands

Question

Exercise:

A car of mass 1500 kg travels along a straight road inclined at 3˚ to the horizontal. The resistance to motion of the car from air and friction is pvN, where v ms^(-1) is the speed of the car and p is a constant. The car travels at a constant speed of 20 ms^(-1) up the slope and the engine of the car works at a constant rate of 21.4 kW.

Calculate the value of p to the nearest whole number.

Aufgabe:

Ein Wagen mit der Masse 1500 kg fährt entlang einer geraden Straße bei 3° Steigung zur Horizontalen. Der Luftwiderstand gegen die Bewegung des Wagens und der Widerstand der Reibung ist pvN, wobei v ms^(-1) die Geschwindigkeit des Fahrzeugs ist und p eine Konstante. Das Auto bewegt sich mit einer konstanten Geschwindigkeit von 20 ms^(-1) den Hang hinauf und der Motor des Autos arbeitet mit einer konstanten Rate von 21,4 kW.

Berechnen Sie den Wert von p auf die nächste ganze Zahl.

Ansatz/Problem:

Ich habe 299,9 heraus, kann das einer überprüfen?

Answer 1

To calculate the value of p, we can use the work-energy principle. The work done by the engine is equal to the change in kinetic energy of the car. The equation for the work done by the engine is W = F d cos(theta), where F is the force exerted by the engine, d is the distance traveled, and theta is the angle of the incline.

The force exerted by the engine is equal to the power output divided by the speed, so F = P/v. The distance traveled is the length of the incline, which is not given in the problem. However, since the car is traveling at a constant speed, we can use the time it takes to travel up the incline to calculate the distance.

We know that the power output of the engine is 21.4 kW, the speed of the car is 20 ms^-1 and the angle of the incline is 3 degrees. We also know that the force resisting motion is pvN.

We can now use the above information to find the value of p to the nearest whole number.

W = F d cos(theta) = (21.410^3)/20 * d * cos(3)
p vN = (21.410^3)/20 * d * cos(3)
p = (21.4*10^3)/20 * d * cos(3) / (vN)

Substituting known values, we get
p = (21.410^3)/20 * d * cos(3) / (1500 * 20)
p = (21.410^3) * d / (30,000)

Since we don't know the distance traveled, we can't calculate the exact value of p. However, we can say that p is around 0.0714.