A car that weighs 15,000 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.
Make certain you convert the weight 15000N to mass.
Force= .5 M V^2/distance=
= .5 (Weight/g)V^2 /distance3=
= .5(15,000/9.8)*16.66^2 /30
and that gives the right answer.
Force x (stopping distance)
= (initial kinetic energy)
= (1/2) M V^2
For the kinetic energy, you will have to convert the weight (N) to mass (kg) and the 60 km/hr initial velocity to m/s. I assume you know how to do this.
Your answer, MV^2/(2X) will be in Newtons.
Thanks you for your quick reply. I really appreciated it, although I still cannot find the way to get the answer which is 7,086.7 N.
m = 15,000/9.8 = 1530 kg
v = 60,000 m/3600 s = 16.7 m/s
(1/2) m v^2 = 212,500 Joules
F (30) = 212,500
F = 7083 N
To determine the magnitude of the braking force, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
First, let's convert the initial velocity from km/hr to m/s. We know that 1 km/hr is equal to 1/3.6 m/s.
Initial velocity (v1) = 60 km/hr * (1/3.6) m/s = 16.67 m/s
Next, let's calculate the acceleration (a). We can use the following formula:
a = (v2 - v1) / t
Where:
v2 = final velocity, which is 0 m/s since the car comes to a stop.
v1 = initial velocity, which is 16.67 m/s.
t = time taken to bring the car to a stop, which is given as 30 m.
Now, let's substitute the values into the formula:
a = (0 m/s - 16.67 m/s) / 30 m
= -16.67 m/s / 30 m
= -0.5567 m/s^2 (negative sign indicates deceleration)
We have the acceleration value. Now, we can use the weight of the car to find the magnitude of the braking force.
Weight (W) = mass (m) * gravitational acceleration (g)
= m * 9.8 m/s^2
To find the mass of the car (m), we can rearrange the equation:
m = W / g
= 15,000 N / 9.8 m/s^2
= 1530.61 kg
Now, we can calculate the magnitude of the braking force (F) using Newton's second law:
F = m * a
= 1530.61 kg * -0.5567 m/s^2
= -850.66 N (Note: The negative sign indicates that the force is in the opposite direction of motion, which is necessary to bring the car to a stop)
Therefore, the magnitude of the braking force is approximately 850.66 N.