So in physics lab we did an experiment with a cart with two different masses on a air track (practically eliminating kinetic friction). The track was tilted at 4 degrees. Using 4 photo-gates I got the speed of both gliders and the height at each point. I made two graphs making height my x and velocity squared y. Both slopes are negative. Does that seem correct?
Also these questions I need assistance in. Could someone please help me?
1) How does mass affect height and velocity squared relationship?
Since there is no kinetic friction this question confuses me.
2)What physical property does the slope of the height vs. v^2 graph represent? Should slope be positive or negative?
I got a negative slope for both hopefully I have assumed correctly to put height in x and velocity in y. But I don't understand what they mean by physical property?
c) What physical property does the vertical intercept represent?
yet again with the physical property thing..
Any sort of help would be appreciated! Thank you for taking the time to read this.
Im starting to guess that for question one would velocity be independent of mass
I asked someone else about two and they said the slopes should be neg because dv/dt = -g and since gravity is always downward then slope is neg.
As for the property I'm still not sure.
sliding down from height 1 to height 2- conservation of energy gives:
(1/2) m v2^2 - (1/2) m v1^2 = m g( h1-h2)
Mass cancels out
so
v2^2 - v1^2 = -2 g (h2 - h1)
v2^2 = v1^2 - 2g(h2-h1)
note
negative slope, as height goes down, speed goes up
if you start out at h1 = h2, then v2 = v1 .
for an object simply dropped through height h, v = sqrt(2 g h)
at t = 0 when h2 = h1
at t = 0 when h2 = h1
v2 = v1
usually v1 is zero but maybe not in your experiment which means the zero of velocity is the height the puck would have been dropped from at zero speed down
Okay its starting to make sense to me now. Thanks for taking the time to explain this to me!
In order to understand the relationships between mass, height, and velocity squared in your experiment, let's break down the questions:
1) How does mass affect the height and velocity squared relationship?
To analyze the effect of mass on the relationship between height and velocity squared, you should plot separate graphs for each mass and compare the results. In your case, you would have two sets of data for the two different masses. By plotting height on the x-axis and velocity squared on the y-axis for each mass, you can examine if there are any differences between the two graphs.
If the two graphs have different slopes, it implies that mass does affect the relationship between height and velocity squared. If the slopes are similar, it suggests that mass does not have a significant influence on this relationship.
2) What physical property does the slope of the height vs. v^2 graph represent? Should the slope be positive or negative?
In physics, the slope of a graph represents the rate of change between the variables on the x-axis and y-axis. In this case, the slope of the height vs. v^2 graph represents the change in velocity squared for a given change in height. A negative slope means that as the height increases, the velocity squared decreases. This implies that there is a relationship between height and velocity squared, and as the cart moves higher on the tilted track, its velocity squared decreases.
c) What physical property does the vertical intercept represent?
The vertical intercept on the height vs. v^2 graph represents the v^2 value when the height is zero. In other words, it represents the initial velocity squared of the cart. The physical property associated with the vertical intercept is the initial kinetic energy of the system.
Remember that when interpreting these graphs and relationships, it's essential to consider the experimental setup, the conditions (such as eliminating kinetic friction), and any other relevant factors that might influence the results.