How Is Engine Power Related to Velocity and Resistive Force in Automobiles?

[mjdiaz89]

Homework Statement

The engine of an automobile requires 40 hp to maintain a constant speed of 78 km/h.

(a) What is the resistive force against the automobile?
correct check mark
1376.465N (correct)
(b) If the resistive force is proportional to the velocity, what must the engine power be to drive at constant speeds of 65 km/h?
wrong check mark
hp
(c) What must the engine power be to drive at constant speeds of 145 km/h under the same conditions?
wrong check mark
hp

Homework Equations

P=Fv = $$\frac{Fd}{s}$$

The Attempt at a Solution

Questions B and C: It seems I have two unknowns (Resistive force and engine power output). Any ideas?

 

[lavalamp]

Since you are assuming that resistive force is directly proportional to velocity, you know:
$$F \propto v$$
$$F = kv$$

Therefore:
$$P = Fv$$
$$P = kv^{2}$$

You now need to find the constant k, then you'll be all set.

 

[Moetasim]

I would approach this problem by first understanding the concepts of force, velocity, and power. Force is a physical quantity that causes an object to accelerate or change its motion. In this case, the resistive force is the opposing force that the engine must overcome to maintain a constant speed of 78 km/h.

Velocity is the rate of change of an object's position over time. In this scenario, the velocity is given as 78 km/h.

Power is the rate at which work is done or energy is transferred. In this case, it is the amount of energy needed to maintain a constant speed of 78 km/h.

For question A, to find the resistive force, we can use the equation P=Fv, where P is the power, F is the force, and v is the velocity. Rearranging the equation, we get F=P/v. Substituting the given values, we get F=40hp/78 km/h = 0.51 hp. To convert this to Newtons, we use the conversion factor 1 hp = 746 Nm/s, which gives us a resistive force of 1376.465N.

For questions B and C, we can use the same equation P=Fv, but this time we are given different velocities. Since we know the power output of the engine (40 hp), we can rearrange the equation to find the required force at each velocity. So for question B, F=(40hp)/(65 km/h) = 0.62 hp. And for question C, F=(40hp)/(145 km/h) = 0.28 hp.

In conclusion, to maintain a constant speed of 78 km/h, the engine requires 40 hp of power to overcome a resistive force of 1376.465N. For different velocities, the required force changes, but the power output of the engine remains the same.