A car of mass 1300 kg is driving along a road at speed of 28m/s. As it approaches some traffic lights, the lights change to red and the driver applies his brakes causing the car to skid. The frictional force between the skidding tyres and the road is 0.8 of the weight of the car. Caculate how far the car will travel before it stops?
I have calculated the distance to be 199.796m S=(V^2-V^2)/2a
& a = (F-X)/m = -1.962m/s/s
Are my calculations correct?
Any help would be greatly appreciated.
Best regards Sean
Wc = M*g = 1300 * 9.8 = 12,740 N. = Normal force, Fn.
Fp = Mg*sin A = Mg*sin 0 = 0. = Force parallel to the plane.
Fk = u*Fn = 0.8 * 12,740 = 10,192 N.
a = (Fp-Fk)/m = (0-10,192)/1300 = -7.84 m/s^2.
d = (Vf^2-Vo^2)/2a = (0-(28^2))/-15.68 = 50 m.
Your calculations are almost correct, but there is a minor mistake in the formula you used to calculate the distance. Let me explain the correct steps to calculate the distance the car will travel before it stops.
1. Calculate the deceleration (negative acceleration) of the car using the frictional force and the mass of the car.
- Frictional force = 0.8 times the weight of the car = 0.8 * (mass of the car * acceleration due to gravity)
- Weight of the car = mass of the car * acceleration due to gravity (9.8 m/s^2)
- Deceleration (a) = Frictional force / mass of the car (since the force is in the opposite direction of motion)
2. Use the initial velocity (v = 28 m/s) and the deceleration (a) to calculate the distance (s) travelled before the car stops.
- Use the equation: v^2 = u^2 + 2as
where v = final velocity (0 m/s since the car stops), u = initial velocity (28 m/s), a = deceleration, and s = distance. Rearranging the equation:
s = (v^2 - u^2) / (2a)
Let's plug in the values and calculate the distance:
1. Deceleration:
Frictional force = 0.8 * (1300 kg * 9.8 m/s^2) = 10144 N
Deceleration (a) = Frictional force / mass of the car = 10144 N / 1300 kg = 7.803 m/s^2
2. Distance:
s = (0^2 - 28^2) / (2 * -7.803)
= (0 - 784) / (-15.606)
= (-784) / (-15.606)
= 50.267 m
So, the car will travel approximately 50.267 meters before it comes to a complete stop.
Therefore, the correct answer is around 50.267 meters, not 199.796 meters.