Download Net Force and Acceleration

Net Force and Acceleration
Purpose: To determine the acceleration of gravity using Newton’s second law.
Equipment: air track assembly, weight set, wood block, meter stick, smart pulley interface.
Discussion: Newton’s second law predicts the behavior of objects under the influence of a net force:
Fnet=ma. Net force is the sum of all forces acting on a mass: Fnet = ΣF. Consider the setup for todays lab.
Mass “M”, the glider on the air track, is being accelerated by the tension or force of the string attached
to it. The tension is the result of the force gravity “Fg” pulling downward on the driving mass “m”. The
string pulls on the glider “M” with force “ T”. “M”’s inertia resists the force and slows the acceleration of
the system. Both masses must be accelerated by the force of gravity on “m”.
∑F = T-T+mg = mg (direction of motion is positive)
T
M
Fnet = (M+m)a
(M+m)a=mg
a = mg/(M+m)
m
T
As “M” gets larger, “a” decreases. As
“M” goes to zero, “a” approaches “g”.
Fg=mg
If the air-track is set at an angle “θ”, the net force is either reduced or augmented by the direction and
magnitude of the component of gravity acting on the glider “M”: Fx = Mgsinθ. See your textbook or
check online resources for drawings and details.
M
M
T
Mgsinθ
Mgsinθ
x
θ
Fnet = (M+m)a
mg+Mgsinθ = (M+m)a
T
a = (mg+Mgsinθ)/(M+m)
mg
Mg
For procedure C, a = (mg-Mgsinθ)/(M+m) since gravity is working against the motion.
The acceleration, a, is determined by the interface as described below. You are to solve the
above equation for, g, the acceleration of gravity. A drawing for each procedure is required showing all
forces acting on both masses as well as the application of Newton’s second law to each procedure. You
should clearly show the development of the solution for “g” in Part A, B and C. Show in the calculations
section, your solution for θ in parts B and C.
Procedure: Part A: net force and gravity
1. Air track setup: With no tension on the string, insure that the air track is level by placing the cart, “M”,
near the center and turning the air blower on. Adjust the height of the pulley so that the string is parallel
to the track. Align the track with the pulley.
2. Hang a10.0g mass on the paper clip hanger(1.0g) so that it hangs freely w/o swinging.
3. Open the Newton interface app, click the start button, then release the cart. Click stop when the cart
reaches the end of the track.
4. The app should display a v-t graph of the motion. Select the linear portion of the graph and pull down
the “fit” tab on the graph and choose “linear.” The acceleration is displayed as the slope.
5. Repeat 4 times increasing the hanging mass, “m”, by 10.0g each trial.
6. Using Newton’s second law, solve for the acceleration as a function of “g”, “M” and “m.” (see
principle section above.)
7. Plot acceleration v. m/(M+m). The slope of this graph is your experimental value for “g”. This and the
% error are the result for part A.
Part B: Net force on an incline (downhill)
1. Place the wood block under the end of the air track farthest from the pulley. Calculate the angle of
the air track relative to the table; θ = tan-1(rise/run). The rise is the thickness of the block and the run is
the distance between supports.
2. Use the same procedure as part A to collect acceleration data.
3. Using Newton’s second law, solve for acceleration as a function of “g”, “M”, “m”, and “θ”.
4. Plot acceleration as a function of “M”, “m”, and “θ”. The slope of this graph is your experimental
value of “g”. This and the % error are the result for part B.
Procudure C: Net force on an incline (uphill)
1. Use the same procedure as part B but with the block under the end nearest the pulley. Results are
similar.
Supplemental Questions: (write questions and show all work)
1. In procedure A, when does the tension of the string equal the force of gravity; before and/or after
movement begins? explain.
2. In procedure A, if the cart and hanging mass are equal, what would you expect acceleration to be?
Show using Newton’s 2nd law.
3. In procedure C, use Newton’s second law to determine the mass needed to keep the cart stationary.
Does this seem consistent with your data? If not, explain.