Question

Procedure

M=270 g (hanger +220g); Tape the 220 g to the hanger that is 50g

m=250g (hanger +200g); Tape the 200 g to the hanger that is 50g

Set the apparatus so that when m is on the floor, M is at height h=1.50m; Make sure you measure and record the actual value of h that you use.

Release the system from rest and measure the time taken for m1 to fall on the floor.

SAFETY – When M hits the floor it becomes a free projectile; have a group member catch it!!!!

You will perform 5 trials and record the data in the following

                

Table 1:                                                                                                                                                         

Trial #

Time, second

1

5.55

2

5.43

3

5.71

4

5.38

5

5.66

Data and Calculation

Determine the average time tav from your data in Table 1.

In order to determine the final velocity of mass m1 just before it hits the floor you can use:

Method 1:

It can be shown that the final velocity of the mass m1is given by eq. (1):

h=12(vi+vf)t eq. (1)

Method 2:

Since mass M started from rest we could also use

vf=vi+at eq. (2)

The following equation for the acceleration of the Atwood machine can be derived using FBD:

a=M-mM+mg eq. (3)

Calculating Energy

Calculate the final kinetic energy KEf , and the final potential energy PEf using the following equations:

KEf=12(M+m)vf2 eq. (4)

PE=mgh                    eq. (5)

The final total energy is given by:

Ef=Kf+PEf             eq. (6)

(Note: mass needs to be in kilograms if you are reporting the energy in units of Joules).

Record the final velocity, obtained using Method 1 and Method 2 in Table 2 below.

Table 2:

Method #

vf, m/s

1

2

Using the equations above, compute the initial and final total mechanical energy of the system for each of the final velocities (from Method 1 and Method 2) and record your results in Table 3 below.

Table 3:

Method #

Ei=PEi+Ki

(J)

Ef=PEf+Kf

(J)

Percentage difference

1

2

If total energy is conserved, then Ei=Ef. Find the percentage difference between the two measured values of Ei and Ef, using the following formula:

%difference = Ei-EfEi+Ef2×100

Analysis:

Answer the following questions:

Based on your experiment would you conclude that the mechanical energy was conserved?

How much (if any) energy was lost (or gained)?

Where did the energy go or come from?

What are the sources of error?

Which of the two methods used to compute the final velocity is better suited for this experiment and why?

Based on your knowledge of principle of conservation of mechanical energy when forces are conservative, answer the following conceptual questions using the words - increase, decrease, or         remains the same. Refer to figure 1. The gravitational potential energy reference level will be the ground as indicated by y=0.

As m rises, what happens to its gravitational potential energy?__________

As M falls, what happens to its gravitational potential energy? __________

As the masses move what happens to the total gravitational potential energy of the system? __________

As M falls, what happens to its kinetic energy? __________

As m rises, what happens to its kinetic energy? __________

As the masses move what happens to the total kinetic energy of the system? __________

Assuming no friction, as m rises and M falls, what happens to the total mechanical energy of the system? __________

Determine your own power rating by measuring the time it takes you to climb a flight of stairs. Ignore the gain in kinetic energy.   Do 5 trials and submit the table below.    Outline the strategy for obtaining your data and provide the calculations you used to determine you power (hint: refer to example 7.11 in the text).

Trial #

Time, second

1

2

3

4

5

Answer 1

Analysis:

Answer the following questions:

Based on your experiment would you conclude that the mechanical energy was conserved?

yes we can say that the mechanical energy is conserved because in method-1 it decreased and in method-2 it increased which is due to the error.

How much (if any) energy was lost (or gained)?

method-1 : 0.22 joules was lost

method-2 : 0.86 joules was gained

Where did the energy go or come from?

some energy went to the surrounding air.

What are the sources of error?

measurment of height h and time t.

Which of the two methods used to compute the final velocity is better suited for this experiment and why?

method-2 is better because final velocity is calculated using h and t both of them are measured. While in method-1 t was measured but acceleration a was a theoretical value which was calculated without taking the air resistance into account.

Based on your knowledge of principle of conservation of mechanical energy when forces are conservative, answer the following conceptual questions using the words - increase, decrease, or         remains the same. Refer to figure 1. The gravitational potential energy reference level will be the ground as indicated by y=0.

As m rises, what happens to its gravitational potential energy?__increase________

As M falls, what happens to its gravitational potential energy? ______decrease____

As the masses move what happens to the total gravitational potential energy of the system? ___decrease

As M falls, what happens to its kinetic energy? ______increase____

As m rises, what happens to its kinetic energy? _____increase_____

As the masses move what happens to the total kinetic energy of the system? ____increase______

Assuming no friction, as m rises and M falls, what happens to the total mechanical energy of the system? __remains the same________