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?
1. if they have the same energy (work) put into them, they have the same KE. How could one gain more than the other?
2. If the mass is 2x, and the KE is the same, then the V^2 of the faster car is 2x, or V is sqrt2 faster. If they were in the air (falling) the same time, then it would go 10sqrt2 distance.
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 Honda Civic actually has greater kinetic energy at the edge of the cliff. The kinetic energy is given by the equation KE = (1/2)mv^2, where m is the mass of the car and v is its velocity.
While it is true that the Lincoln Town Car has twice the mass of the Honda Civic, this does not necessarily mean it will have twice the kinetic energy. Kinetic energy also depends on velocity. Since both cars are accelerated across equal distances, the Honda Civic will have a higher velocity at the edge of the cliff due to its lower mass. Therefore, the Honda Civic has greater kinetic energy.
This answer does not contradict the explanation for Question 2 because the impulse imparted to a car only depends on the force and the time interval over which the force is applied. It does not consider mass or velocity. So, even though the Lincoln Town Car has a larger impulse, it does not necessarily mean it will have greater kinetic energy.
Now, let's move on to your second question:
2.) Suppose the slower car (Lincoln Town Car) crashes at a horizontal distance of 10m from the ledge. At what horizontal distance does the faster car (Honda Civic) hit?
To solve this question, we need to consider the motion of the cars in the air after the applied force is suddenly removed. We assume no air resistance or other external forces acting on the cars.
Since we are ignoring the effects of friction, the horizontal motion of the cars is independent of their vertical motion. Therefore, the only factor affecting the horizontal distance is the initial velocity of each car.
Given that the Lincoln Town Car crashes at a distance of 10m, this means that its horizontal velocity was constant and equal to the velocity it had at the edge of the cliff.
As the Honda Civic is accelerated across the same distance, it has a higher velocity than the Lincoln Town Car. Therefore, it will cover the same distance of 10m in less time. Since its time of flight is shorter, it will travel a shorter horizontal distance.
So, the faster car (Honda Civic) will hit at a horizontal distance less than 10m from the ledge. The exact distance depends on the specific velocities and time intervals involved, but it will be less than 10m.