Name: _____________________ Class: Physics 214
SSN/ID:   _____________________ Section & Group: ____________
Lab 2 - Acceleration due to gravity

Objective
The idea of this lab is to measure the acceleration of an object (car on an inclined ramp) due to the force of gravity. This acceleration (called 'g') does not depend on the mass of the object if the effect of friction is small.

Equipment
Motion car, weights (washers), ramp, photogate & timer interface, and a protractor.

Definition
The idea in this lab is to determine the acceleration due to gravity and to see if it truly is 9.8m/s2. The acceleration due to gravity is symbolized by the letter g (Note: the letter g does NOT stand for grams!) and is measured in units of m/s2, or: 


     [meters]
------------------
[second · second]
The way you'll calculate this acceleration due to gravity is to first determine the velocity at two different points. Remember, the velocity, in this case, is just the speed of the particle at two different points. Speed is simply the: 

                       [change_in_distance]
speed (or velocity) = ----------------------
                         [change_in_time]
and is symbolized by: v = Δd/Δt. Acceleration, on the other hand, is simply the change in speed (either the increase or decrease): 

                [change_in_velocity]
acceleration = ----------------------,
                  [change_in_time]
is symbolized by: a = Δv/Δt, and is measured in units of m/s2.

Procedure

  1. Setup the ramp and the stand.

  2. Measure the inclination of the ramp with the protractor.

  3. Setup the photogate clamps on the ramp as shown below (use a separation of 40cm between the two clamps) and connect the timer as shown.

    The car fits into the keyhole at the top of the ramp and the "wing" should point to the side with the clamps so that, as it moves, the wing passes through them. The photogate contains a photoelectric cell which provides a signal to the timer when something interrupts or changes the beam path.

    This signal can be used to give the time interval it takes for the wing on the car to move through one of the photogates or the time it takes for it to move from the first gate to the second gate down the ramp.

  4. To make the measurements simultaneously, set the timer to interval mode. In this mode, the timer displays the time interval within clamp A (must have only button A depressed), the time in clamp B (must have only button B depressed), or the time between the two clamps (must have both buttons A & B depressed).
  5. Since the width of the wing on the car is 5-cm (0.05-m), we can use the times "through the clamps A and B" to determine the average velocity at A and B from the relation velocity = distance/time. These numbers are very close to the instantaneous velocity at each clamp (since v is close to constant; recall that average velocity = instantaneous velocity only when velocity = constant and also that the slope of the distance vs. time graph always gives you the instantaneous velocity).

    Velocity at A (va) = 0.05m/(time_through_A)
    Velocity at B (vb) = 0.05m/(time_through_B)

    The average velocity (in meters/sec) for the trip from A to B as the car runs down the ramp is given by:

    
                       velocity_at_A + velocity_at_B
    Average velocity = -----------------------------  meters/sec
                                     2
  6. If we measure the distance between A and B (call it dab) and measure the time it takes the car to move between A and B (call it tab), we also determine the average velocity for the trip. The values will be the same as we find in the item above:
    
                        Distance_from_A_to_B
    Average velocity = ----------------------  meters/sec
                       Time_taken_from_A_to_B
  7. Since we have the velocity at A and at B and we also know the time it takes, we can calculate the acceleration down the ramp as follows:

    acceleration: a = ( vb - va ) / tab meters/sec/sec
  8. This acceleration down the ramp is due to the force of gravity. If we ignore the friction between the car and the track, the acceleration due to gravity down a ramp inclined at an angle θ is given by:

    a = g sin(θ)

    where g is the acceleration due to gravity "g" (the value you would get if you drop something vertically). The value of g = 9.8 meters/sec/sec. See:

  9. From your measurements of a, and knowing the inclination of the ramp θ, you can calculate a value for g and see how it compares with the known value of 9.8 m/sec/sec. Calculate the relative difference between your value and the known value using:
    
                          9.8 m/s2 - Your_value_for_g
    Relative Difference = ----------------------------  x 100%
                                   9.8 m/s2
  10. Perform the experiment for another inclination of the ramp (if the first run was at 30o, try the second one at 40o or 50o). When you finish taking the data for the second run, add some weight (the washers) to the car and repeat the experiment at that same angle.

    Your measurement of acceleration should be the same as for the car without washers.
  11. The mass of the car is 364-grams (0.364-kg) without washers and 410-grams with 11 washers added to it.
  12. Did you notice any trend in your data as the ramp becomes more vertical? Should there be? Why?
  13. Is there any significant difference in your measurements for the car with different weights?
# Physical Values Run
  1     2     3  
1 Car's mass m [grams]      
2 Time for car's wing to go through Gate A: Δta [s]      
3 Velocity through A: va [m/s]      
4 Time through B: Δtb [s]      
5 Velocity through B: vb [m/s]      
6 Time to go from A to B: Δtab [s]      
7 Distance from A to B: dab [m]      
8 vavg (using (va + vb)/2) [m/s]      
9 vavg (using dab/Δtab) [m/s]      
10 a (using (vb - va)/Δtab) [m/s2]      
11 Angle of inclination, θ [o]      
12 g (using a/sinθ) [m/s2]      
13 Relative Difference [%]