Question

A car of weight 2240 n operating at a rate of 112 kw develops a maximum speed of 41 m/s on a level, horizontal road. assuming that the resistive force (due to friction and air resistance) remains constant, what is the car’s maximum speed on an incline of 1 in 20; i.e., if θ is the angle of the incline with the horizontal, sin θ = 1 20 ? answer in units of m/s.

Answer 1

To find the car's maximum speed on an incline of 1 in 20, we need to calculate the resistive force on the incline. By using the weight of the car and the angle of the incline, we can determine this force. Then, by dividing the power of the car by the resistive force, we can find the car's maximum speed on the incline.

Step-by-step explanation:

To calculate the car's maximum speed on an incline of 1 in 20, we need to consider the forces acting on the car. In this case, the two main forces are the gravitational force (mg) and the resistive force (due to friction and air resistance). On the horizontal road, the resistive force is equal to the weight of the car, which is 2240 N. On the incline, the resistive force is equal to the weight of the car multiplied by the sin of the angle of the incline. Therefore, the resistive force on the incline is given by:

Resistive force = (2240 N) * sin(θ)

Since θ is equal to 1/20, or 0.05 radians, we can substitute this value into the equation:

Resistive force = (2240 N) * sin(0.05 radians)

To find the car's maximum speed on the incline, we divide the power (112 kW) by the resistive force:

Maximum speed = (112 kW) / Resistive force