A car with a mass of 5 tons is moving uphill with an acceleration of 0.2 m / s. Find the traction force
A car with a mass of 5 tons is moving uphill with an acceleration of 0.2 m / s. Find the traction force if sina = 0.02 and the drag coefficient is 0.04
Given:
m = 5 tons = 5000 kilograms – vehicle weight;
a = 0.2 m / s2 – acceleration with which the car is moving;
sin (a) = 0.02 – sine of the slope of the mountain;
k = 0.04 is the value of the resistance coefficient.
It is required to determine F (Newton) – the traction force of the car.
According to the condition of the problem, the car is moving uphill (upward). Then, according to Newton’s second law:
F – F friction = m * a;
F – k * N = m * a;
F – k * m * g * sin (a) = m * a, where g = 10 m / s2 is the acceleration of gravity;
F = m * a + k * sin (a) * m * g;
F = m * (a + k * sin (a) * g);
F = 5000 * (0.2 + 0.04 * 0.02 * 10) = 5000 * (0.2 + 0.04 * 0.2) = 5000 * (0.2 + 0.008) =
5000 * 0.2008 = 1040 Newton.
Answer: the pulling force will be equal to 1040 Newtons.
