CONSTANT ACCELERATION

 

GOAL

            To study how the acceleration of an object moving down an incline depends on the angle of incline.

 

PREREQUISITES

                                 R.D. Knight, Physics for scientists and engineers, chapter 5.

 

EQUIPMENT

                         Air track with cart (or board with cart)

                         Meter Stick

                         Stopwatch

                         High Spacer Blocks

 

THEORY

                 A cart on an incline rolls down due to the gravity force (weight of the car). The acceleration due to gravity is constant and straight down as shown below.

 

The component of gravity force, parallel to the inclined surface is m·g·sinθ. Thus, a cart on the incline possess the acceleration g·sinθ, neglecting friction. The sine of the angle θ (sinθ) can be found from the height and the length of the incline  

 

sinθ = height / length of track

 

 

PROCEDURE

1.      Set the cart on the horizontal air track against the bottom end stop and record this final position of the cart.

2.      Set the cart on the horizontal air track at the initial position (at opposite side of the air track) and record this initial position of the cart.

3.      Set up track as shown on the Figure below, using one block to raise the end of the track. Measure the vertical height of the cart in the initial position.

4.      Release the cart from rest and use the stopwatch to time how long it takes to cart to hit the end stop. The person who releases the cart should also operate the stopwatch. Repeat this measurement five times and record data in the Table below.

5.      Measure the vertical height of the cart in the final position.

6.      Add one block to increase the height of the air track and repeat steps 3-5.

7.      After adding all three blocks put upper block vertically and repeat steps 3-5. Do the same for two blocks in the vertical position. The total number of measurements at different initial height has to be 4-5.

 

 

 

ANALYSIS

                        Initial position of the cart __________________________________

 

                        Final position of the cart ___________________________________

 

                        Displacement of the cart d __________________________________

 

 

Height at top

(m)

 

 

 

 

 

Height at bottom  (m)

 

 

 

 

 

Δh

 

 

 

 

 

Trial 1

T (s)

 

 

 

 

 

Trial 2

T (s)

 

 

 

 

 

Trial 3

T (s)

 

 

 

 

 

Trial 4

T (s)

 

 

 

 

 

Trial 5

T (s)

 

 

 

 

 

Average T

(s)

 

 

 

 

 

sinθ=Δh/d

 

 

 

 

 

Acceleration

a=2d/T2

 

 

 

 

 

 

  1. Fill in the Table.
  2. Put acceleration points versus sinθ on the graph below.
  3. Draw the graph acceleration versus sinθ.
  4. Find the slope of the graph.
  5. What number do you have to end up with for the slope in ideal situation?
  6. Why is your slope different? Write a short (5-6 sentences) essay about the possible origins of this difference.