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
D. Inertia, F
E. Tractive Resistance/Effort
To determine the various resistances and effort for the given scenario, we will use the equations of motion and relevant formulas.
A. Gradient Resistance, Rg:
The gradient resistance is the force experienced by the car due to the inclination of the slope. It can be calculated using the formula:
Rg = (m * g * sin(θ))
Where,
m = mass of the car = 1045 kg
g = acceleration due to gravity = 9.8 m/s^2
θ = angle of the slope in radians = arctan(grade) = arctan(14.5/100)
First, convert the angle from degrees to radians:
θ = arctan(14.5/100) = 0.1489 radians
Then calculate the gradient resistance:
Rg = (1045 kg) * (9.8 m/s^2) * sin(0.1489)
B. Rolling Resistance, Rrl:
The rolling resistance is the force due to the friction between the tires of the car and the road surface. It can be calculated using the formula:
Rrl = (m * g * cos(θ)) * coef_rl
Where,
coef_rl = coefficient of rolling resistance
Given that the coefficient of rolling resistance is not provided, we cannot calculate Rrl without this value.
C. Aerodynamic Resistance, Ra:
The aerodynamic resistance is the force experienced by the car due to air resistance. It can be calculated using the formula:
Ra = 0.5 * ρ * v^2 * Cd * Af
Where,
ρ = air density = 1.2 kg/m^3
v = velocity of the car
Cd = drag coefficient = 0.45
Af = frontal area of the car = 2.62 m^2
v = distance / time = 680 m / 50 s
Calculate the aerodynamic resistance:
Ra = 0.5 * (1.2 kg/m^3) * ((680 m / 50 s) / 3.6)^2 * (0.45) * (2.62 m^2)
D. Inertia, F:
The inertia force is the force required to accelerate the car. It can be calculated using the equation:
F = m * (change in velocity / time)
Change in velocity = final velocity - initial velocity
Given that the car speeds up from 0 km/h to 74 km/h in 50 seconds, convert the velocities to m/s and calculate F.
E. Tractive Resistance/Effort:
The tractive resistance or effort is the sum of the gradient resistance, rolling resistance, aerodynamic resistance, and inertia force. It can be calculated using the equation:
Tractive Resistance = Rg + Rrl + Ra + F
Without the value of the rolling resistance coefficient (coef_rl), we cannot calculate the tractive resistance/effort.
To complete the calculations, you will need to provide the value of the coefficient of rolling resistance (coef_rl).