Measuring Acceleration (SQA National 5 Physics): Revision Note

Measuring acceleration

• Acceleration is the rate of change of velocity, or the change in velocity per unit time

• The quantities required to determine the acceleration of a moving object are

  • the initial velocity $u$ of the object

  • the final velocity $v$ of the object

  • the time interval $t$ between these velocities

• The experimental methods for measuring acceleration are similar to those used for measuring speed

• Apparatus for measuring acceleration:

  • Trolley

  • Ramp

  • Card with one or two sections attached to the trolley

  • Ruler

  • Stop clock

  • One or two light gates connected to a computer or electronic timers

Measuring acceleration with one light gate

Acceleration from rest

• This method uses one light gate and a single card to measure acceleration

• Method:

  • Set up the ramp with one light gate (attached to a computer or timer) at the bottom of the ramp

  • Measure the length of the card $d$ using a ruler

  • Release the trolley from rest (initial velocity $u=0$) at the top of the ramp and start the stop clock

  • As the trolley passes the light gate, the timer records the time $t_1$ the card blocks the light beam

  • Use the stop clock to measure the time $t_2$ for the trolley to reach the light gate

  • Calculate the final velocity $v$ using the equation:

  $v=\frac{d}{t_1}$

  • Calculate the acceleration $a$ of the trolley using the equation:

  $a=\frac{v}{t_2}$

Acceleration at a point

• This method uses one light gate and a double card (two sections separated by a gap) to measure acceleration at a single point

• Method:

  • Set up the ramp with one light gate (attached to a computer) at any point

  • Measure the length $d$ of each mask using a ruler (ideally, these should be the same length)

  • Release the trolley from rest at the top of the ramp

  • As the trolley passes the light gate, the computer records the time $t_1$ that the first card blocks the light beam and the time $t_2$ that the second card blocks the light beam

  • The computer also records the time $t$ between each card passing through the light beam

  • Calculate the initial velocity $u$ using the equation:

  $u=\frac{d}{t_1}$

  • Calculate the final velocity $v$ using the equation:

  $v=\frac{d}{t_2}$

  • Calculate the acceleration $a$ of the trolley at a point using the equation:

  $a=\frac{v-u}{t}$

Measuring acceleration with two light gates

• This method uses two light gates and a single card to measure the average acceleration between two points

• Method:

  • Set up the ramp with two light gates (attached to a computer or timers) at the bottom of the ramp

  • Measure the length of the card $d$ using a ruler

  • Release the trolley from rest at the top of the ramp

  • As the trolley passes through light gate 1 and light gate 2, times $t_1$ and $t_2$ are recorded, respectively, as the card blocks the light beam

  • Use the stop clock to measure the time $t$ for the trolley to pass between the light gates

  • Calculate the initial velocity $u$ using the equation:

  $u=\frac{d}{t_1}$

  • Calculate the final velocity $v$ using the equation:

  $v=\frac{d}{t_2}$

  • Calculate the average acceleration $\overline{a}$ of the trolley using the equation:

  $\overline{a}=\frac{v-u}{t}$

Evaluating the experiment

• The main source of error in these experiments arises from human error in the measurements of

  • distance, when using a ruler

  • time, when using a stop clock

• The experiments could be improved by

  • using an electronic timer instead of a stop clock to record the time $t$ between the gates

  • releasing the trolley from the same point each time

  • taking repeat readings and averaging the results