What constant net force is required to bring a 1500 kg car to rest from a speed of 100 km/h within a distance of 55 m?
To determine the constant net force required to bring a car to rest, we can use the equation for work:
Work = Force × Distance
Work is the change in kinetic energy of the car. In this case, the car is initially moving with a certain kinetic energy and needs to bring it to zero, indicating that the total work done by the net force is equal to the initial kinetic energy of the car:
Work = Initial Kinetic Energy
The initial kinetic energy (K.E) of the car can be calculated using the equation:
K.E = (1/2) × mass × velocity^2
Where:
- K.E is the initial kinetic energy,
- mass is the mass of the car, and
- velocity is the initial velocity of the car.
Since the car needs to come to rest, the final velocity (vf) will be 0 m/s. The initial velocity (vi) can be converted from km/h to m/s:
vi = (100 km/h) × (1000 m/km) × (1 h/3600 s)
Now we can calculate the initial kinetic energy:
K.E = (1/2) × (mass) × (vi)^2
Next, we can calculate the work done by the net force:
Work = K.E = (1/2) × (mass) × (vi)^2
Finally, we divide the work by the given distance to obtain the constant net force required:
Force = Work / Distance = ((1/2) × mass × (vi)^2) / Distance
Plugging in the values:
mass = 1500 kg
vi = (100 km/h) × (1000 m/km) × (1 h/3600 s)
Distance = 55 m
We can now calculate the constant net force.
To determine the required net force, 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:
F_net = m * a
In this case, we need to bring the car to rest, which means the final velocity (Vf) will be zero. The initial velocity (Vi) is given as 100 km/h. We also know the distance (d) over which the car comes to rest, which is 55 m. We need to calculate the acceleration first.
To convert the initial velocity from km/h to m/s, we divide it by 3.6:
Vi = 100 km/h = (100 * 1000) m/3600 s = 27.8 m/s
The final velocity is zero, so Vf = 0 m/s.
Using the equation of motion:
Vf^2 - Vi^2 = 2a * d
0^2 - (27.8 m/s)^2 = 2a * 55 m
-27.8^2 = 2a * 55
Simplifying the equation:
-771.84 = 110a
Dividing by 110:
a ≈ -7 m/s^2
Since the car is coming to a stop, the acceleration is negative.
Now, we can calculate the net force needed:
F_net = m * a
F_net = 1500 kg * -7 m/s^2
F_net = -10,500 N
Therefore, a constant net force of -10,500 Newtons is required to bring the 1500 kg car to rest from a speed of 100 km/h within a distance of 55 m.
100 km/h = 100000m/3600s = 27.8 m/s
Vf^2 = Vi^2+2as
The final velocity, Vf, is 0
0 = (27.8m/s)^2 + (2)(55m)(a)
Solve for the acceleration, a.
F = ma
Use the acceleration from the previous step and the mass given to get the force, F.