a car that weighs 15000 N is initially moving at 60 km/hr when the brakes are applied. The car is brought to a stop in 30 m assuming the force applied by the brakes is constant determine the magnitude of the braking force
convert the km/hr to m/s
find the mass of the car
find the KE of the car ... the work done stopping the car is equal to the KE
work = braking force * stopping distance
To determine the magnitude of the braking force, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
First, let's convert the initial velocity from km/hr to m/s:
60 km/hr = 60,000 m/3600 s = 16.67 m/s
Next, we need to calculate the deceleration or negative acceleration of the car:
The final velocity is 0 m/s (since the car is brought to a stop). Let's assume the car decelerates with a constant acceleration of "a" m/s^2.
Using the equation of motion: v_f^2 = v_i^2 + 2ad, where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and d is the distance covered.
0^2 = (16.67 m/s)^2 + 2a(30 m)
0 = 278.89 m^2/s^2 + 60a
Rearranging the equation, we get:
60a = -278.89
Dividing both sides by 60:
a = -4.65 m/s^2
Since the acceleration is negative, it means the car is decelerating.
Now, let's calculate the mass of the car using the weight formula:
Weight = mass × acceleration due to gravity
The weight is given as 15,000 N, and the acceleration due to gravity is approximately 9.8 m/s^2.
15,000 N = mass × 9.8 m/s^2
Rearranging the equation to solve for mass:
mass = 15,000 N / 9.8 m/s^2
mass ≈ 1530.61 kg
Finally, we can calculate the magnitude of the braking force using Newton's second law:
Force = mass × acceleration
Force = 1530.61 kg × -4.65 m/s^2
Force ≈ -7,124 N
The magnitude of the braking force is approximately 7,124 N.
To determine the magnitude of the braking force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the car that weighs 15000 N, and we need to find the braking force.
First, let's convert the initial velocity from km/hr to m/s. This can be done by dividing 60 km/hr by 3.6 (since there are 3.6 seconds in an hour) to get:
Initial velocity = 60 km/hr ÷ 3.6 = 16.67 m/s
Next, we need to find the acceleration of the car. We can use the kinematic equation:
v² = u² + 2as
where:
v = final velocity (0 m/s, since the car comes to a stop)
u = initial velocity (16.67 m/s)
a = acceleration
s = displacement (30 m)
Rearranging the equation to solve for acceleration (a), we get:
a = (v² - u²)/(2s)
a = (0 m/s)² - (16.67 m/s)² / (2 * 30 m)
a = (-277.7 m²/s²) / 60 m
a = -4.63 m/s²
Since the car is decelerating or slowing down, the acceleration is negative.
Finally, we can calculate the magnitude of the braking force using Newton's second law:
Force = mass * acceleration
Since weight is the force exerted on an object due to gravity, we can find the mass of the car using the equation:
Weight = mass * acceleration due to gravity
mass = Weight / acceleration due to gravity
mass = 15000 N / 9.8 m/s²
mass ≈ 1531.63 kg
Now we can calculate the magnitude of the braking force:
Force = mass * acceleration
Force = 1531.63 kg * (-4.63 m/s²)
Force ≈ -7091.6 N
Therefore, the magnitude of the braking force is approximately 7091.6 N. Notice that the negative sign indicates that the force is in the opposite direction of motion, which makes sense since the car is decelerating.