Solving a Lab to Place the Cup for the Ball

[Goodwillie7]

Homework Statement

I have a lab to do in which we have a ramp set up on a table. We are rolling the ball down the ramp, and letting it roll of the table. We have to figure out where to place the cup for the ball to roll into. If we do not get the ball in the cup we fail. How can I do that?

Homework Equations

All I know is the Initial velocity will be 0, since we are placing the ball at the top of the ramp then letting go. And once the ball rolls of the table, Acceleration is going to be -9.8m/s (squared)

The Attempt at a Solution

I would find the measurements of the ramp, the distance from the bottom of the ramp, to the end of the table, and the height of the table itself. Then use equations, but I don't know which ones.

 

[Astronuc]

Height of the ramp determines the GPE of the ball with respect to the table top, and that will be transformed into KE, from which one obtains a velocity in the horizontal, v_x.

When the ball leaves the table it falls under influence of gravity, so one must determine v_y(t), with v_y(0) = 0.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra11

and since the ball is rolling, there is rotational as well as translation KE.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi

 

[m2003]

As a scientist, there are several steps you can take to solve this lab and determine the placement of the cup for the ball to roll into.

1. Measure the ramp: As you mentioned, the first step would be to measure the ramp and determine its length and angle of incline. This will help you determine the initial velocity of the ball as it rolls down the ramp.

2. Calculate the initial velocity: Using the measured distance and the acceleration due to gravity (-9.8m/s^2), you can calculate the initial velocity of the ball using the equation v = √(2gh), where v is the initial velocity, g is the acceleration due to gravity, and h is the height of the ramp.

3. Determine the horizontal distance: Once you have the initial velocity, you can use the equation d = vt to calculate the horizontal distance the ball will travel before reaching the edge of the table. Here, d represents the horizontal distance, v is the initial velocity, and t is the time it takes for the ball to reach the edge of the table.

4. Find the placement of the cup: Using the calculated horizontal distance, you can determine the placement of the cup by measuring the distance from the edge of the table and placing the cup at that point. Alternatively, you can use the equation d = ½at^2 to calculate the time it takes for the ball to reach the edge of the table, and then use this time to determine the placement of the cup.

5. Repeat for accuracy: To ensure accuracy, you can repeat the experiment multiple times and adjust the placement of the cup accordingly. You can also make adjustments to the initial velocity by changing the angle of the ramp and repeating the calculations.

Overall, the key equations to use in this lab would be v = √(2gh) and d = vt or d = ½at^2. By accurately measuring and calculating these values, you can determine the placement of the cup for the ball to successfully roll into.