a car which weight is 1000N is travelling at 90kmn/hr and come to rest in a distance of 50m after applying the brakes. assume uniform acceleration, calculate how large its stopping force was exerted by the friction between the wheel and the road.
90,000 meters / 3600 seconds = 25 m/s=Vi
v = Vi + a t
0 = 25 + a t
so a t = -25 and t = -25/a
d = Vi t + .5 a t^2
50 = 25 (-25/a) + .5 a (625/a^2)
50 = -625/a + .5 (625/a)
50= -625/2a
100 a = -625
a = -6.25
then
F = m a
To calculate the stopping force exerted by the friction between the wheel and the road, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration (F = m * a). In order to use this equation, we need to find the mass of the car and the acceleration it experienced.
First, let's convert the car's speed from km/h to m/s:
90 km/h * (1000 m/1 km) * (1 h/3600 s) = 25 m/s
Next, we need to find the acceleration. We can use the equation of motion which relates distance, initial velocity, final velocity, and acceleration: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. In this case, the car starts at a speed of 25 m/s and comes to a rest, so the final velocity is 0 m/s and the distance is 50 m. Plugging these values into the equation, we can solve for acceleration:
0^2 = 25^2 + 2 * a * 50
0 = 625 + 100a
-625 = 100a
a = -6.25 m/s^2
Since the car is coming to rest, the acceleration is negative, indicating deceleration.
Now that we have the acceleration, we need to find the mass of the car. We can use the equation F = m * a and rearrange it to solve for mass:
F = m * a
1000 N = m * -6.25 m/s^2
m = -1000 N / -6.25 m/s^2
m = 160 kg
Finally, we can calculate the stopping force using the mass and acceleration:
F = m * a
F = 160 kg * -6.25 m/s^2
F = -1000 N
Therefore, the stopping force exerted by the friction between the wheel and the road is 1000 N.