A car that weighs 14600.0 N is initially moving at a speed of 58.0 km/hr when the brakes are applied and the car is brought to a stop in 4.7 s. Find the magnitude of the force that stops the car, assuming it is constant.
To find the magnitude of the force that stops the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration.
First, we need to convert the car's weight from Newtons to kilograms, since the formula requires mass in kilograms. We can do this by dividing the weight by the acceleration due to gravity (9.8 m/s^2):
Weight = 14600.0 N
Mass = Weight / Acceleration due to gravity
Mass = 14600.0 N / 9.8 m/s^2
Mass = 1489.8 kg (rounded to 3 decimal places)
Next, we need to convert the initial speed from kilometers per hour to meters per second, since the formula requires speed in meters per second. We can do this by multiplying the speed (in km/hr) by 1000/3600:
Initial speed = 58.0 km/hr
Initial speed = 58.0 km/hr * (1000 m / 3600 s)
Initial speed = 16.111 m/s (rounded to 3 decimal places)
To find the acceleration of the car, we can use the formula:
Acceleration = (Final speed - Initial speed) / Time
The car comes to a stop, so the final speed is 0 m/s.
Final speed = 0 m/s
Time = 4.7 s
Acceleration = (0 m/s - 16.111 m/s) / 4.7 s
Acceleration = -16.111 m/s / 4.7 s
Acceleration = -3.431 m/s^2 (rounded to 3 decimal places)
Now, we can use Newton's second law of motion to find the force:
Force = Mass * Acceleration
Force = 1489.8 kg * -3.431 m/s^2
Force = -5101.488 N (rounded to 3 decimal places)
The magnitude of the force that stops the car is 5101.488 N.
To find the magnitude of the force that stops the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's convert the speed of the car from km/hr to m/s, as the unit of force is Newtons (N) which is the standard unit in the SI system.
1 km/hr = 1000 m/3600 s
Therefore, 58.0 km/hr = (58.0 * 1000) / 3600 m/s
Now, we need to calculate the acceleration of the car. Since the car is brought to a stop, its final velocity will be zero. The initial velocity is given as 58.0 km/hr, which we just converted to m/s. The time taken to stop the car is 4.7 s.
The equation we can use to calculate acceleration is:
a = (v_f - v_i) / t
where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time taken.
Plugging in the values:
a = (0 - 58.0 m/s) / 4.7 s
Now we can calculate the acceleration.
a = -12.34 m/s^2
The negative sign indicates that the car is decelerating (slowing down).
Now, we can use Newton's second law to find the force acting on the car.
F = m * a
where F is the force, m is the mass, and a is the acceleration.
Given that the weight of the car is 14600.0 N, we know that weight is equal to mass multiplied by the acceleration due to gravity, 9.8 m/s^2. So, we can calculate the mass of the car.
Weight = m * g
14600.0 N = m * 9.8 m/s^2
m = 14600.0 N / 9.8 m/s^2
m = 1490.8 kg (approximately)
Now, we can find the force that stops the car.
F = m * a
F = 1490.8 kg * -12.34 m/s^2
F = -18387.7 N
The magnitude of the force that stops the car is 18387.7 N.