Thank you so much bobpursley for all your help. I actually think I'm beginning to understand, physics involves a lot of what I've learned so far, Newton's laws, mass, acceleration, etc... I just have to make connections.
“A Honda Civic and Lincoln Town Car are initially at rest on a horizontal parking lot at the edge of steep cliff. The Town Car has twice as much mass as the Civic. Equal constant forces are applied to each car and they accelerate across equal distances (ignore effects of friction.) When they reach the far end of the lot the force is suddenly removed, whereupon they sail through the air and crash on the ground below.”
Question 1 Answer:
1.) Which car has the greater work done on it by the applied force? Explain your answer in terms of distance traveled.
**They are both the same because work=the force x the distance and the force plus the distance is the same for both.
Question 2 Answer:
2.) Which car has the larger impulse imparted to it by the applied force? Explain your answer.
**The Lincoln Town Car because it is heavier, so acceleration is a=f/m, the acceleration is lower and therefore you spend more time on the ground.
I have two more questions:
1.) Which car has the greater kinetic energy at the edge of the cliff? Does your answer follow from your explanation 0f 1? Does it contradict your answer to 2? Why or why not?
**The Lincoln has the larger kinetic energy because it is heavier therefore 2x the mass = 2x the kinetic energy. No it does not follow my answer from 1 because both cars have the same work applied, but the Lincoln has more kinetic energy. My answer does not contradict because the Lincoln has 2x the mass and less acceleration.
2.) Suppose the slower car (Lincoln Town Car) crashes a horizontal distance of 10m from the ledge, at what horizontal distance does the faster car hit, (Honda Civic)?
**I think it hits at 20m because if the Lincoln is landing closer to the lot and the mass is 2x then of the civic and the civic goes out faster and has a less mass, wouldn’t you double the 10m?
To answer your first question:
1.) Which car has the greater kinetic energy at the edge of the cliff? Does your answer follow from your explanation of 1? Does it contradict your answer to 2? Why or why not?
The car with greater mass, which is the Lincoln Town Car, will have a greater kinetic energy at the edge of the cliff. This follows from the equation for kinetic energy: KE = (1/2)mv^2, where m is the mass and v is the velocity. Since the Lincoln Town Car has twice the mass of the Honda Civic, it will have twice the kinetic energy.
This answer does not contradict the explanation for question 2. In question 2, we determined that the Lincoln Town Car has a larger impulse imparted to it by the applied force. Impulse is defined as the change in momentum, which is equal to the force multiplied by the time interval during which the force is applied. The larger mass of the Lincoln Town Car results in a smaller acceleration and a longer time interval for the force to be applied. This longer time interval allows the Lincoln Town Car to have a greater impulse, despite having the same applied force and distance traveled as the Honda Civic.
Now, for your second question:
2.) Suppose the slower car (Lincoln Town Car) crashes a horizontal distance of 10m from the ledge, at what horizontal distance does the faster car hit (Honda Civic)?
Since both cars have equal constant forces applied to them and they accelerate across equal distances, it can be assumed that they have the same initial velocity. We can use the equation of motion, s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
Since both cars have equal constant forces applied, their magnitudes of acceleration are the same. However, the Lincoln Town Car has twice the mass of the Honda Civic, which means the acceleration for the Lincoln Town Car will be half of that for the Honda Civic.
Let's assume the time it takes for the Lincoln Town Car to crash is t. Therefore, the time it takes for the Honda Civic to hit the ground will be 2t, since its acceleration is double.
We know that the distance traveled by the Lincoln Town Car is 10m, so we can substitute the values into the equation for the Lincoln Town Car:
10 = (1/2)at^2
Now, substituting the value of acceleration for the Lincoln Town Car (which is half of that for the Honda Civic):
10 = (1/2)(0.5a)t^2
Simplifying:
20 = at^2
Since the time for the Honda Civic is 2t, we can substitute this value into the equation for the Honda Civic:
d = ut + (1/2)at^2
d = 0(2t) + (1/2)a(2t)^2
d = 2at^2
Substituting the equation for acceleration (2a) and the value for the distance traveled by the Lincoln Town Car (10m):
d = 2(20)
d = 40m
Therefore, the faster car (Honda Civic) hits the ground at a horizontal distance of 40m from the ledge.
1.) Which car has the greater kinetic energy at the edge of the cliff? Does your answer follow from your explanation of 1? Does it contradict your answer to 2? Why or why not?
The Honda Civic actually has the greater kinetic energy at the edge of the cliff, not the Lincoln Town Car. This is because kinetic energy is given by the equation KE = 1/2 * mass * velocity^2, and velocity is the same for both cars as they have traveled the same distance and experienced the same force. Since the Lincoln Town Car has twice the mass of the Honda Civic, according to the equation, it should have twice the kinetic energy. However, this contradicts our answer to question 2, where we stated that the Lincoln Town Car has lower acceleration and spends more time on the ground. So, there is a contradiction between the two answers.
2.) Suppose the slower car (Lincoln Town Car) crashes a horizontal distance of 10m from the ledge, at what horizontal distance does the faster car hit (Honda Civic)?
The faster car, the Honda Civic, would hit the ground at a distance greater than 10m from the ledge. To determine the exact horizontal distance, we need more information about the cars' masses, the force applied, and the time taken for them to reach the edge of the cliff. Without this information, we cannot accurately determine the specific distance at which the Honda Civic hits the ground.