Question

10 балловАвтомобиль массой m = 2000 кг при включенном моторе спускается 0,03 с с постоянной скоростью v=15 м/с. При какой мощности двигателя он может равномерно подниматься вверх по такому же уклону с такой же скоростью?

Answer 1

M=2000 кг     v=15 м/с     tgα=0.03    P=?
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При движении с горы с выключенным двигателем
Fтр=m*g*sinα
При малых углах sinα≈tgα
При движении в гору сила тяги
Fт=Fтр+m*g*tgα=2*m*g*tgα
Мощность
P=Fт*v=2*m*g*v*tgα=2*2000*10*15*0.03=18*10^3 Вт
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Answer 2

Calculating the Power Needed to Ascend an Incline

To calculate the power needed for the car to ascend an incline at a constant speed, we can use the formula:

Power = Force × Velocity

Where: - Force is the force required to overcome the gravitational force and the force of friction on the incline. - Velocity is the speed at which the car is ascending the incline.

Calculating the Force Required

The force required to overcome the gravitational force and the force of friction on the incline can be calculated using the formula:

Force = Weight × (sin(θ) + μcos(θ))

Where: - Weight (W) is the weight of the car, which is equal to the mass of the car multiplied by the acceleration due to gravity (W = m × g). - θ is the angle of the incline. - μ is the coefficient of friction.

Given: - Mass of the car, m = 2000 kg - Acceleration due to gravity, g = 9.8 m/s^2 - Angle of the incline, θ = sin^-1(0.03) (since the car is descending at an angle of 0.03 radians) - Coefficient of friction, μ (not provided)

Calculating the Power

Using the calculated force and the given velocity, we can then calculate the power needed for the car to ascend the incline at a constant speed.

Let's proceed with these calculations.