a 1500 kg automobile is travelling upto 20 degrees inclined at a speed of 6m/s. if the driver wishes to stop his car in a distance of 5m, determine the frictional force at pavement which must be supplied by rear wheels
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KE=PE+W(fr)
m•v²/2 =m•g•h+F(fr) •s,
F(fr) =m(v²/2•s – g/ siná)
To determine the frictional force at the pavement that must be supplied by the rear wheels, we need to consider the forces acting on the car and use the laws of motion.
First, let's draw a free body diagram to identify the forces acting on the car:
1. Weight (mg): This force acts vertically downward and is equal to the mass (m) of the car multiplied by the acceleration due to gravity (g = 9.8 m/s²).
Weight (mg) = 1500 kg * 9.8 m/s²
2. Normal force (N): This force is perpendicular to the incline and acts perpendicular to the surface of the inclined plane. It is equal in magnitude but opposite in direction to the component of the weight acting perpendicular to the incline.
Normal force (N) = mg * cos(θ), where θ is the angle of inclination (20 degrees).
3. Frictional force (f): This force acts parallel to the incline and opposes the car's motion. It is the force that the rear wheels must supply to stop the car.
We need to find the frictional force (f).
Using the equation of motion, we can calculate the frictional force:
Initial velocity (u) = 6 m/s
Final velocity (v) = 0 m/s (since the driver wants to stop the car)
Distance (s) = 5 m
The equation of motion is:
v² = u² + 2as
Here, v = 0 m/s, u = 6 m/s, and s = 5 m. We need to solve for a.
0² = (6 m/s)² + 2a(5 m)
0 = 36 m²/s² + 10a
-10a = 36 m²/s²
a = -36 m²/s² / 10
a = -3.6 m/s²
We find that the deceleration is -3.6 m/s².
Now, we can calculate the normal force (N) and the frictional force (f):
Normal force (N) = mg * cos(θ)
Normal force (N) = 1500 kg * 9.8 m/s² * cos(20 degrees)
Frictional force (f) = m * a
Frictional force (f) = 1500 kg * (-3.6 m/s²)
Finally, we have the values for the normal force (N) and the frictional force (f) at the pavement, which must be supplied by the rear wheels.