a car that weights 15000 N is initially moving at 60 km/hour when the brakes are applied. The car is brought to a stop at 30 meters. Determine the magnitude of the braking force
To determine the magnitude of the braking force, we need to calculate the acceleration of the car first using the given information.
1. Convert the initial velocity from km/h to m/s:
The initial velocity is 60 km/h. To convert this to m/s, multiply it by 1000/3600 (since there are 1000 meters in a kilometer and 3600 seconds in an hour):
Initial velocity = 60 km/h × (1000 m/1 km) × (1 h/3600 s) = 16.67 m/s (rounded to two decimal places)
2. Now, we can use the kinematic equation to find the acceleration:
v² = u² + 2as
where v is the final velocity (0 m/s since the car is brought to a stop), u is the initial velocity (16.67 m/s), a is the acceleration, and s is the distance covered (30 meters).
Rearranging the equation to solve for acceleration:
a = (v² - u²) / (2s)
a = (0 m/s)² - (16.67 m/s)²) / (2 × 30 m)
a ≈ -5.55 m/s² (negative sign indicates deceleration)
3. Now that we have the acceleration, we can calculate the braking force using Newton's second law of motion:
F = m × a
where F is the force, m is the mass (which can be obtained by dividing the weight by the acceleration due to gravity), and a is the acceleration.
Given weight = 15000 N, and acceleration due to gravity = 9.8 m/s²:
m = weight / gravity
m = 15000 N / 9.8 m/s² ≈ 1530.61 kg (rounded to two decimal places)
F = (1530.61 kg) × (-5.55 m/s²)
F ≈ -8499.32 N (rounded to two decimal places)
The magnitude of the braking force is approximately 8499.32 N. Note that the negative sign indicates that the force is in the opposite direction of motion, representing deceleration.