A car of mass 100kg travelling with a velocity of 20mls was suddenly brought to rest 20m after application of break, find the average ating force and power expended by the engine.?
average speed during stop = 20/2 = 10 m/s
went 20 meters so it took 2 seconds
change in momentum/time = force
100 * 20 / 2 = 1,000 Newtons
power = change in energy/time = (1/2)(100) (20^2) /20= 10,000 watts
or power = force * distance /time = 1000*20 /2 = 10,000 watts
Thanks so much damon.
Given: M = 100 kg, Vo = 20 m/s.
V^2 = Vo^2 + 2a*d = 0.
20^2 + 2a*20 = 0,
400 + 40a = 0,
a = -10 m/s^2.
F = M*a = 100 * (-10) = -1,000 N. The negative sign means the force opposed the action.
V = Vo + a*t = 0.
20 + (-10)t = 0,
t = 2 s.
P = F*d/t = 1000 * 20/2 = 10,000 Joules/s = 10,000 Watts.
To find the average retarding force and power expended by the engine, we can use the equations of motion.
1. Average retarding force (F):
The retarding force can be found using Newton's second law of motion: F = ma, where F is the force, m is the mass of the car, and a is the acceleration.
Given:
Mass of the car (m) = 100 kg
Final velocity (v) = 0 m/s
Initial velocity (u) = 20 m/s
Distance traveled (s) = 20 m
To find the acceleration, we can use the equation:
v^2 = u^2 + 2as
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / 2s
Substituting the values:
a = (0^2 - 20^2) / (2*20)
Calculate the value:
a = -400 / 40 = -10 m/s^2
Since the car is being brought to rest, the acceleration is negative.
Now, substituting the mass and acceleration values into Newton's second law of motion:
F = m * a
= 100 kg * -10 m/s^2
Calculate the value:
F = -1000 N
Therefore, the average retarding force is -1000 Newtons. The negative sign indicates that the force is acting opposite to the motion of the car.
2. Power expended by the engine (P):
Power can be calculated using the formula: P = F * v, where P is the power, F is the force, and v is the velocity.
Given:
Force (F) = -1000 N
Velocity (v) = 20 m/s
Substituting the values into the formula:
P = -1000 N * 20 m/s
Calculate the value:
P = -20,000 Watts
Therefore, the power expended by the engine is -20,000 Watts. Again, the negative sign indicates that the power is being exerted opposite to the direction of motion.