A 1830-kg car is traveling with a speed of 19.8 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 63.1 m?
Not sure about the equation to use for this queation.
Well, to calculate the magnitude of the horizontal net force required to bring the car to a halt, we can use the equation: force = mass × acceleration.
First, let's calculate the acceleration:
Using the equation v^2 = u^2 + 2as, where u is the initial velocity (19.8 m/s), v is the final velocity (0 m/s since the car is coming to a halt), a is the acceleration, and s is the distance traveled (63.1 m):
0^2 = 19.8^2 + 2a(63.1)
0 = 392.04 + 126.2a
-392.04 = 126.2a
a = -3.1 m/s^2
Now, we can substitute the value of acceleration back into the equation force = mass × acceleration:
force = 1830 kg × -3.1 m/s^2
So, the magnitude of the horizontal net force required to bring the car to a halt is 5,673 N. Now, that's quite a force! It's like trying to stop your friend from eating the last slice of pizza.
To solve this problem, you can use the equations of motion. The equation that relates distance, initial velocity, final velocity, acceleration, and time is:
\[v_f^2 = v_i^2 + 2a \cdot d\]
Where:
- \(v_f\) is the final velocity (in this case, it will be 0 m/s)
- \(v_i\) is the initial velocity (19.8 m/s)
- \(a\) is the acceleration
- \(d\) is the distance (63.1 m)
Since we are interested in finding the net force, we can solve for acceleration and then calculate the net force using Newton's second law:
\[F_{\text{net}} = m \cdot a\]
Step 1: Calculate the acceleration:
Rearrange the equation of motion to solve for the acceleration:
\[a = \frac{{v_f^2 - v_i^2}}{{2 \cdot d}}\]
Substituting the values:
\[a = \frac{{0^2 - (19.8 \, \text{m/s})^2}}{{2 \cdot 63.1 \, \text{m}}}\]
Step 2: Calculate the net force:
Plug in the values of mass (1830 kg) and acceleration (calculated in step 1) into Newton's second law:
\[F_{\text{net}} = (1830 \, \text{kg}) \cdot a\]
Now we can plug in the values to calculate \(F_{\text{net}}\).
To find the magnitude of the horizontal net force required to bring the car to a halt, we can use the concepts of work-energy theorem and Newton's laws of motion.
1. First, we need to calculate the initial kinetic energy of the car:
The formula for kinetic energy is: KE = (1/2) mv^2,
where m is the mass of the car and v is its velocity.
Plugging in the values, we get: KE = (1/2) * 1830 kg * (19.8 m/s)^2.
2. Next, we need to calculate the work done by the net force on the car, which can be determined using the work-energy theorem:
According to the work-energy theorem, the work done on an object equals the change in its kinetic energy.
In this case, since the car comes to a halt, the change in kinetic energy is equal to the initial kinetic energy.
So, the work done by the net force can be written as: Work = KE.
3. Now, we know that work done is defined as the force applied multiplied by the distance over which the force is applied:
Work = Force * Distance.
4. Rearranging the equation, we can solve for force:
Force = Work / Distance.
5. Plugging in the values of work and distance, we can calculate the magnitude of the horizontal net force:
Force = KE / Distance.
So, the equation we can use for this question is: Force = (1/2) * m * v^2 / d.
Let's substitute the given values into the equation to find the answer.