A car that weighs 15,000 N is initially moving at 60km/hr when the brakes are applied. The car is brought to a stop in 30m. Assuming the force applied by the brakes is constant, determine the magnitude of the braking force.
Vf^2=Vi^2 + 2ad
but a= force/mass
so when you finally solve this, force will be negative: what does that mean?
To determine the magnitude of the braking force, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
First, let's convert the initial speed from km/hr to m/s. We can do this by multiplying the speed in km/hr by the conversion factor of 1000 m/1 km and 1 hr/3600s.
Speed = 60 km/hr = (60 × 1000 m) / (1 × 3600 s) = 16.67 m/s (approximately)
Next, let's calculate the acceleration of the car. We can use the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s), u is the initial velocity (16.67 m/s), a is acceleration, and s is the displacement.
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
a = (0^2 - 16.67^2) / (2 × 30)
a = (-277.56) / 60
a = -4.626 m/s^2 (approximately, the negative sign indicates deceleration)
Now, let's calculate the magnitude of the braking force using Newton's second law.
F = m × a
Given that the weight of the car is 15,000 N, we can divide this by the acceleration due to gravity (g ≈ 9.8 m/s^2) to find the mass of the car:
mass (m) = weight (W) / acceleration due to gravity (g)
m = 15,000 N / 9.8 m/s^2 = 1,530 kg (approximately)
Finally, we can calculate the magnitude of the braking force:
F = m × a = 1,530 kg × (-4.626 m/s^2) = -7,066.8 N (approximately)
The magnitude of the braking force is approximately 7,066.8 N. Note that the negative sign indicates that the force is in the opposite direction of motion.