A car traveling 72.0 km/h along a straight, level road is brought uniformly to a stop in a distance of 40.0 m. If the car weighs 8.8 x 103 N, what is the braking force?
To find the braking force, we can use the formula:
Frictional force = mass x acceleration
First, let's find the deceleration (acceleration) of the car:
Initial velocity (u) = 72.0 km/h
Final velocity (v) = 0 km/h (since the car stops)
Distance (s) = 40.0 m
1. Convert the initial velocity from km/h to m/s:
u = 72.0 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 20.0 m/s
2. Use the formula to find the acceleration:
v^2 = u^2 + 2as, where v = 0
0 = (20.0 m/s)^2 + 2a(40.0 m)
400.0 m^2/s^2 = 80a
a = 400.0 m^2/s^2 / 80 = 5.0 m/s^2
Now that we have the acceleration, we can find the mass of the car using the weight and acceleration due to gravity:
Weight (W) = 8.8 x 10^3 N
Acceleration due to gravity (g) = 9.8 m/s^2
3. Use the formula to find the mass:
W = mg
8.8 x 10^3 N = m * 9.8 m/s^2
m = (8.8 x 10^3 N) / (9.8 m/s^2) = 897.96 kg (approximately)
Lastly, calculate the frictional force:
Frictional force = mass x acceleration
Frictional force = (897.96 kg) x (5.0 m/s^2)
Frictional force = 4489.8 N (approximately)
Therefore, the braking force is approximately 4489.8 N.
To find the braking force, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In this case, we need to find the acceleration.
We know the initial velocity (v0) of the car is 72.0 km/h, which can be converted to m/s by multiplying by 1000/3600 (since there are 1000 meters in a kilometer and 3600 seconds in an hour).
So, v0 = 72.0 km/h * (1000 m/1 km) * (1 h/3600 s) = 20.0 m/s.
The final velocity (v) of the car is 0 m/s since it comes to a stop.
We also know the displacement (Δx) of the car is 40.0 m.
Now, we can use the equation of motion v^2 = v0^2 + 2aΔx to find the acceleration (a).
Plugging in the values, we have 0^2 = (20.0)^2 + 2a(40.0).
Simplifying the equation, we get 400 = 2a(40.0).
Dividing both sides by 2(40.0), we get a = 400 / (2 * 40.0).
Calculating this, we find a = 5.0 m/s^2.
Now we can calculate the braking force (F) using Newton's second law.
F = ma = (8.8 x 10^3 N)(5.0 m/s^2).
Multiplying these values, we find F = 44 x 10^3 N.
Therefore, the braking force is 44,000 N.