A car weighing 1000kg is going up an incline with a slope of 2 in 25 at a steady speed of 18kmph.If g=10m/s2, the power of its engine is
Correct answer is 4kw
Say the process
The answer should be 4kW
But u got 3988. So definitely u need to check ur answer once again
3988 is in watt. So it should be changed to kilowatt.
3988÷1000=3.9
=4kw
I want provess how the 3988 value is came
To calculate the power of the car's engine, we need to know the force acting against the car's motion and the velocity at which it is moving.
First, we need to find the force opposing the car's motion. This force is the component of the gravitational force acting downhill, perpendicular to the incline.
Given:
Mass of the car (m) = 1000 kg
Slope of the incline (θ) = 2 in 25
Acceleration due to gravity (g) = 10 m/s^2
To find the force opposing the car's motion, we can calculate the gravitational force acting downhill using the equation:
Force (F) = mass (m) x acceleration due to gravity (g)
F = 1000 kg x 10 m/s^2
F = 10,000 N
Now, we can calculate the component of the gravitational force acting perpendicular to the incline using:
Force perpendicular to the incline (F_perpendicular) = F x sin(θ)
θ = 2/25, so sin(θ) = sin(2/25)
F_perpendicular = 10,000 N x sin(2/25)
Next, we need to find the work done against this opposing force by the car. The work done is equal to the force multiplied by the distance the car travels along the incline.
Given:
Speed of the car (v) = 18 km/h
Time (t) = 1 hour
To find the distance traveled, we need to convert the speed from km/h to m/s:
Speed (v) = 18 km/h x (1000 m/3600 s)
v = 5 m/s
To find the time (t) in seconds:
t = 1 hour x (60 minutes/1 hour) x (60 seconds/1 minute)
t = 3600 seconds
Next, we can calculate the distance traveled using the equation:
Distance (d) = speed (v) x time (t)
d = 5 m/s x 3600 seconds
d = 18,000 m
Now, we can calculate the work done by the car against the opposing force:
Work (W) = force (F_perpendicular) x distance (d)
W = F_perpendicular x d
Finally, we can calculate the power of the car's engine using the equation:
Power (P) = work (W) / time (t)
P = W / t
Simply substitute the values we calculated earlier to find the power of the car's engine.
Tan A = 2/25 = 0.08, A = 4.57o.
Fp = Mg*sin A = 10,000*sin4.57 = 797.5 N. = Force parallel to incline.
V = 18km/h = 18,000m/3600s. = 5 m/s.
P = Fp*V = 797.5 * 5 = 3988 J./s = 3988 W.