the 1500 kg automobile is travelling up the 20 degree inclined at a speed of 6 m/s , if the driver wishes to stop his car in a distance of 5m , determine the frictional force at the pavement which must be supplied by the rear wheels.
V^2 = Vo^2 + 2ad.
a = (V^2-Vo^2)/2d.
a = (0-36)/10 = -3.6 m/s^2.
Fk = m*a = 1500 * -3.6 = -5400 N. Acting
in opposite direction of motion.
CORRECTION:
PE = KE.
h = 5*sin20 = 1.71 m.
mg*h-Fk*d = 0.5m*V^2.
1500*9.8*1.71-Fk*5 = 0.5*1500*6^2
25,137-5Fk = 27,000
-5Fk = 27000-25,137 = 1863
Fk = -373 N. = Force of kinetic friction.
To determine the frictional force required to stop the car, we need to consider the forces acting on it. Let's break down the problem step by step.
Step 1: Resolve forces on the incline
The force due to gravity acting on the car can be resolved into two components: one parallel to the incline and one perpendicular to the incline.
The component of the force due to gravity parallel to the incline is given by:
Force_parallel = m * g * sin(θ)
Where:
- m = mass of the car (1500 kg in this case)
- g = acceleration due to gravity (approximately 9.8 m/s²)
- θ = angle of the incline (20 degrees in this case)
Step 2: Calculate the force required to stop the car
To bring the car to a stop, the net force acting on it must be in the opposite direction of motion. In this case, the net force is given by:
Net_force = mass * acceleration
Since the car is coming to a stop, the final velocity (vf) is 0 m/s, and the initial velocity (vi) is 6 m/s. The distance (d) is given as 5m.
We can use the following equation to calculate acceleration:
vf² = vi² + 2 * a * d
Plugging in the values:
0² = 6² + 2 * a * 5
Rearranging the equation, we find:
a = -6² / (2 * 5)
Step 3: Calculate the frictional force
To bring the car to a stop, the frictional force provided by the rear wheels must be equal to the net force. Considering that friction opposes the motion, the frictional force can be calculated as:
Frictional_force = Net_force
Frictional_force = -m * a
Substituting the value of acceleration (a) calculated in step 2, we get:
Frictional_force = -1500 kg * (-6² / (2 * 5))
Now we can calculate the frictional force.