= 1703 N
= 1.7 kN
The calculator below can be used to calculate required pulling force to move a body up an inclined plane.
mass of body - m - (kg)
elevation angle - α - (degrees)
friction coefficient - μ - (zero when neglecting friction)
mass of body - m - (slugs)
elevation angle - α - (degrees)
friction coefficient - μ - (zero when neglecting friction)
A body resting on a plane inclined at at an angle α to the horizontal plane is in a state of equilibrium when the gravitational force tending to slide the body down the inclined plane is balanced by an equal and opposite frictional force acting up the inclined plane.
For equilibrium the "angle of response" α can be expressed as:
μ = Fp / Fn = (W sin α) / (W cos α) = tan α (3)
The weight of a Tesla Model X is 2400 kg. The force acting on the car with 5% inclination can be calculated from (1) as
Fp_5% = (2400 kg) (9.81 m/s2) sin (5°)
= 2051 N
The force acting on the car with 10% inclination can be calculated as
Fp_10% = (2400 kg) (9.81 m/s2) sin (10°)
= 4088 N
If the Tesla is moving along the inclined roads with the same speed - the work done by the forces after 1 km can be calculated as
W5% = (2051 N) (1000 m)
= 2051 kJ
W10% = (4088 N) (1000 m)
= 4088 kJ
If the speed of the Tesla is 80 km/h (22.2 m/s) - the time to drive the distance can be calculated as
t80 = (1000 m) / (22.2 m/s)
= 45 s
The power required to move the vehicle (without rolling and air resistance) can be calculated as
P5% = (2051 kJ) / (45 s)
= 45.6 kW
P50% = (4088 kJ) / (45 s)
= 90.8 kW
If the speed of the car is reduced to 60 km/h (16.6 m/s) - the time to drive the distance can be calculated as
t60 = (1000 m) / (16.6 m/s)
= 60.2 s
The power required to move the vehicle (without rolling and air resistance) can be calculated as
P5% = (2051 kJ) / (60.2 s)
= 34.1 kW
P50% = (4088 kJ) / (60.2 s)
= 67.9 kW
Motion - velocity and acceleration, forces and torque.
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