Answer the questions, using complete sentences. When you have finished, submit this assignment to your teacher by the due date for full credit.
Motion in Two Dimensions 1
1. Is the relationship between velocity and centripetal force a direct, linear relationship or is it a nonlinear square relationship? Explain the answer using your graphs of Fc vs. v and Fc vs.v2. What is the precise mathematical relationship between velocity and centripetal force?
The relationship between velocity and centripetal force is a nonlinear square relationship. When we are referring to a graph a straight line would be said to be linear. Looking at our graph we can see that it’s not a straight line thus we know it’s a non linear relationship.
And we know From the formula that the relationship between centripetal force and velocity is that Centripetal Force is directly proportional to velocity squared and that gives us our precise mathematical relationship between the both .
2. [img width="67" height="36" src="file:///C:/Users/Spare/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_s1026">y = mx, to the equation , and explain what the slope of the graph of Fc vs. v2 represents. Remember that the m in the equation for a line represents the slope, and the m in the centripetal force equation
represents the mass of the stopper.
Answer: Our equation shows us that Centripetal Force the and the square of velocity have a direct proportion
Which means as one is increased the other increases as well considering r in that case is constant.
This is verified by our centripetal force vs velocity square graph where as we plot the points we can see this direct relationship between the points and the graph will give us a straight line.
This means that this relationship is linear.
The equation y=mx has a graph which has a line with a positive slope that passes through the origin where y is proportional to x and the proportion constant would be m.
We can see that centripetal force and Velocity squared are also proportional
v squared by r is equal to centripetal acceleration so we can say that Centripetal force is Proportional to Centripetal acceleration where m is the constant
The slope of Fc/v^2 is basically m which represents the mass/r which is the radius
So we can deduct that the slope of the graph for the equation Fc vs. v2
represents the ratio between mass and the radius (lenght of the chain in this case
3. If you shorten the length of the chain, keep other variables constant, and repeat the experiment, how will the centripetal force change? Explain the relationship between centripetal force and the length of the chain.
Answer:From our equation we can see that Centripetal force is inversely proportional to the radius or the length of the chain in our case
So if we are planning to keep all the variables constant and only change the r value by decreasing it
This will mean a larger centripetal force will be needed to for an object with the same mass and velocity.
Motion in Two Dimensions 2
4. Complete the tables.
Answer: degree of elevation: 4.7
Length of ramp (cm)
Average drop time (s)
Average distance the ball traveled (m)
Horizontal velocity (m/s)
5. For each angle of elevation, what is the relationship between the velocity of the ball and the distance (x) that the ball traveled?
Answer: What we can say is that the angle of the ramp could have determined the speed of the ball increasing proportionally. The table provides us with evidence that the length of ramp did have an effect on the average distance the ball had travelled. WE can see that, the further done the ball was brown at , the longer it had travelled when reaching the ground . This is due to the fact that when the balls speed increased, the kinetic energy acting upon it also increase and as the kinetic force increased, the friction force also increased. The angle of elevation determines how quickly the ball could travel down the ramp, the more slanted that ramp is the faster the ball can go through the ramp and also create a higher average distance travelled by ball. This is how they are all linked together. The more the less time the average drop took, the more average distance the ball travelled, which further resulted in a higher horizontal velocity as the horizontal velocity was calculated via dividing the average distance the ball traveled by the average drop time.