A car with mass of 1045 kg speeds up to 74 km/h until reaching the top of hill in 50 s and covered distance of 680 m. The slope of the hill is 14.5 % grading. Given that the frontal area of the car, Af=2.62 m2, air density, ρ=1.2 kg/m3 and drag coefficient is 0.45. Take g=9.8 m/s2, determine
A. Gradient Resistance, Rg
B. RollingResistance,Rrl
C. Aerodynamic Resistance, Ra [1 mark] D. Inertia, F
E. Tractive Resistance/Effort
To determine the different resistances and effort associated with the car's movement, we can use the following formulas:
A. Gradient Resistance, Rg:
Rg = mass * g * sin(theta)
where mass is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the slope given as a percentage.
Given:
Mass (m) = 1045 kg
Slope (theta) = 14.5% = 0.145
Rg = 1045 kg * 9.8 m/s^2 * 0.145
Rg = 1527 N
B. Rolling Resistance, Rrl:
Rrl = mass * g * cos(theta) * u
where u is the coefficient of rolling resistance.
Given:
Coefficient of rolling resistance (u) is not provided. Typically, u ranges between 0.01 to 0.03 for general car tires. You need to use the appropriate value based on the specific conditions and type of tires involved.
C. Aerodynamic Resistance, Ra:
Ra = 0.5 * Cd * Af * ρ * v^2
where Cd is the drag coefficient, Af is the frontal area of the car, ρ is the air density, and v is the velocity of the car.
Given:
Drag coefficient (Cd) = 0.45
Frontal area (Af) = 2.62 m^2
Air density (ρ) = 1.2 kg/m^3
Velocity (v) = distance / time
Distance (d) = 680 m
Time (t) = 50 s
v = d / t
v = 680 m / 50 s
v = 13.6 m/s
Ra = 0.5 * 0.45 * 2.62 m^2 * 1.2 kg/m^3 * (13.6 m/s)^2
Ra = 18.48 N
D. Inertia, F:
F = mass * acceleration
where acceleration = change in velocity / time
Change in velocity (Δv) = v - 0 (initial velocity is assumed to be 0)
F = mass * (Δv / t)
F = 1045 kg * (13.6 m/s / 50 s)
F = 283.52 N
E. Tractive Resistance/Effort:
Tractive Resistance/Effort = Rg + Rrl + Ra + F
Substituting the calculated values:
Tractive Resistance/Effort = 1527 N + Rrl + 18.48 N + 283.52 N
Please note that the value for Rrl depends on the coefficient of rolling resistance (u) and it is not provided in the given information. To complete the calculation, you need to substitute the appropriate value or considera range based on tire specifics and conditions.