need help with physics question

Question

We literally just started this chapter and I can't register a single thing in my brain. Pls help out

A cylindrical object can roll down an incline. The incline is slightly less than one meter in length. A group of students wants to determine the acceleration of the object while it is rolling down the incline. The students have access to the following equipment.

• A stopwatch, which can measure time intervals up to 999 s with a precision of 0.01 s

• A clock, which can measure time intervals up to 12 hours with a precision of 1 minute (60 s)

• A meterstick, which can measure lengths up to 1 m with a precision of 1 mm

• A pair of calipers, which can measure lengths up to 10 cm with a precision of 0.05 mm

(a) Assume the object moves with a constant acceleration as it rolls down the incline. Write an equation that includes acceleration and quantities that can be measured or obtained from measurements by using the available equipment in the list.

(b) Design an experimental procedure that could be used to measure the quantities required to determine the acceleration of the object.

List the quantities and associated symbols that would be measured and the equipment used to measure them. Also list the equipment that would be used to measure each quantity.

Describe the overall procedure to be used

(c)

i. What quantities could be graphed to yield a straight line that could be used to determine the acceleration of the object? Only indicate quantities that either were measured in part (b) or could be determined from quantities measured in part (b).

-------------Vertical axis 

-------------Horizontal axis

ii. How could the graph be used to analyze the data and determine the acceleration?

(d) After rolling down the incline, the cylindrical object rolls across a horizontal surface, as shown in. The object then hits a vertical wall and bounces off the wall with the same speed it had before hitting the wall. Note that during the bounce the object is in contact with the wall for a time interval that is very small, but not zero.

During the time the object is in contact with the wall, is the magnitude of the acceleration greater than, less than, or the same as it was while it was rolling down the ramp?

Briefly explain your reasoning.

Answer 1

a) This equation here is one of a few kinematic equations (kinematic, meaning related to motion) and it's one of the most used equations in introductory physics courses:

1. x_f – x_i = v_i • t + 1/2 a • t ²
2. x_f is the location of the cylinder at the bottom of the ramp, or its final coordinate
3. x_i is the starting spot of the cylinder on the ramp, or its initial location
4. » Often, the left side of the equation: (x_f – x_i) is simply called Δx for displacement (the difference, in length, between where the object started and where it ended up).
5. v_i is the object's initial velocity. We can assume that, in this case, it is 0, meaning that the students just let the cylinder roll down without being pushed.
6. t is the time variable. At the moment the cylinder is let go, t = 0
7. Finally, a is the acceleration (the value we want to know) that will be calculated from the measured t from the stopwatch and Δx displacement of the cylinder.

In your problem, Δx length difference between the cylinder's start and the bottom of the ramp.

b)

Step 0 is to put the calipers away and to use the clock only to see when your class gets out. The calipers, although more precise, are too short a measuring tool to be useful. The clock is too imprecise.

1. Measure the length of the ramp with the meter stick. This length is Δx_ramp
2. Get one student to hold the cylinder at the top of the ramp while a second prepares the stopwatch.
3. Start the stopwatch when Student #1 lets go of the cylinder and stop it when the cylinder is observed to hit the bottom of the ramp. Record the time as t
4. Repeat steps 2-3 starting the cylinder at 8 different locations up the ramp besides the top, recording Δx and t for each trial (Note: I chose 8 to give us enough data points for part c)

Hopefully this provides enough for the how-to

c)

We're going to need a different equation here because Δx = 1/2 a • t ² gives us a parabola graph when we put Δx on the y-axis (confusing, I know. But that's actually where it goes): and t on the x-axis SO here a linear kinematic equation:

v = v_i + a • t

The v stands for velocity (speed with a direction) at some time t. We know v_i = 0 cm/s, we're still looking for a, and we just measured t, but we don't have v yet: only Δx.

Thankfully, we have a relation for v in terms of Δx.

v = Δx / t

For each of the 8 spots you chose on the ramp to roll down the cylinder, plot ( Δx / t ) which equals v on the y-axis and t on the x-axis and you have you straight line. You now know the speed of the cylinder at times t and the slope of that line is a.

d)

Just like v = Δx / t acceleration a = Δv / t. Let's look at the ramp acceleration a_ramp first: Since the cylinder starts off at rest though we know that Δv_ramp is just the velocity of the cylinder rolling on the floor v_floor . The time it accelerated is t_measured , the time you wrote down from your stopwatch.

Now the Δv_wall is the velocity difference between the cylinder rolling into the wall, v_floor , and it rolling out, -v_floor . The difference is 2 • v_floor . The time it's in contact with the wall is nonzero, but more importantly it's very small! So short of a time that it's difficult - if not impossible - to measure with a stopwatch. Let's write this out:

Δv_ramp = v_floor < 2v_floor = Δv_wall

t_ramp = t_measured > t_{too small to measure} = t_wall

a = Δv / t So a_wall > a_ramp

Hope this helps!!