Help with lab - final velocity of total distance

[texan717]

Homework Statement

All right so this will probably sound a little muddled but I'll try anyway. We conducted a lab today in class. We were given a hot wheels car, a meter stick, a ramp, and a stopwatch. We were told to find final velocity of total distance. We were not told how to actually perform this lab. Our teacher is really into making us think about how to find your answer. Anyway we decided to time how long it took the car to go down the ramp from the top to the bottom. So my first question is that right?

Assuming yes,
ramp = 51 cm in length
height = 10 cm
average time was .86 s

Homework Equations

y = 1/2 + at^2
vf^2 = vi^2 + 2ax

The Attempt at a Solution

All right so I can form a triangle. The vertical component is 10 cm, the hypotenuse is 51 cm.
Using the pythagorean theorem I get 50.01 cm for the horizontal. That doesn't seem to help me much. I tried using vf^2 = vi^2 + 2ax.
Initial velocity is zero. 2 * gravity * .51 m = 10.0062
The squr root of 10.0062 is 3.16 m /s. Is this the amount of vertical velocity ?

I really could use some help to know if I'm anywhere near the correct way to solve this.

 

[rl.bhat]

Along the ramp the acceleration is less than g. Find the angle of inclination of the ramp. Then find the component of g along the ramp. Use this value in the equation you have written to find the final velocity.

 

[tomcue]

As a scientist, it is important to understand the concepts behind the experiment and how to properly analyze the data collected. In this case, it seems like you are on the right track in terms of using the equations for motion to calculate the final velocity. However, there are a few points that need to be clarified.

Firstly, when using the equation vf^2 = vi^2 + 2ax, it is important to note that the acceleration (a) in this case is the acceleration due to gravity (g), which is approximately 9.8 m/s^2. Therefore, the correct calculation would be vf^2 = 0 + 2(9.8)(0.51), which gives a final velocity of 3.14 m/s.

Secondly, the value you calculated for the vertical velocity is actually the acceleration due to gravity (g), not the vertical velocity. The vertical velocity would be the final velocity in the y-direction, which can be calculated using the equation vf = vi + at. In this case, the initial velocity (vi) is also 0, so the final velocity in the y-direction would also be 3.14 m/s.

Lastly, it is important to note that the final velocity calculated using the equations for motion is the total velocity of the car, not just the vertical component. This is because the car is moving in both the x and y-directions. If you want to calculate the vertical component of the velocity, you can use the equation vy = (vf^2 - vix^2)^1/2, where vix is the initial velocity in the x-direction (which is also 0 in this case).

In conclusion, it seems like you have a good understanding of the concepts and equations involved in this experiment. However, it is important to carefully consider the units and values being used and make sure they are consistent. I would recommend discussing your approach and calculations with your teacher to ensure that you have a complete understanding of the experiment and its results.