Force and Acceleration RP

This practical is about testing Newton's Law -> . You could be investigating either:

-> how force affects acceleration

• Independent variable (what I change) = resultant force

• Dependent variable (what we measure) = acceleration

• Control variable (what is kept the same) = mass

-> or how mass affects acceleration

• Independent variable = mass

• Dependent variable = acceleration

• Control variable = resultant force

Equipment:

In either experiment, the easiest way to test the relationships is to use a trolley on a track.

To apply a force to the trolley, to move it along, we attach a string with masses attached to the trolley and hang it over a pulley. The force applied to the trolley through the tension in the string is found from the downward force of gravity exerted on the masses,

To see how force affects acceleration, we could either use a stopwatch and calculate the acceleration using our acceleration equations, or we could use a light gate that is connected to a computer that calculates the acceleration for us as long as we tell the computer the length of the trolley and the distance between the two light gates.

Stopwatch Version:

• Set up your equipment as shown above, with a string attached to the front of a toy car that hangs over the edge of the table, over a pulley with masses attached. Measure and mark on the table a distance for the trolley to travel, around works well.

• Hold the car at the start, then release it while starting your stopwatch

• Stop the stopwatch when the trolley reaches the end of the marked distance

• Remove masses from the weight stack (e.g. reduce from to , then , etc.), ensuring that you add the removed masses to the top of the toy car each time. This is to ensure the total mass of the system is kept constant. And repeat the steps above.

To calculate the acceleration of the trolley, you need to use the acceleration equation:

Formula:

The initial velocity of the toy car will be as it is held at rest, so we need to find the final velocity of the trolley in order to calculate the acceleration as the time will be the time recorded on the stopwatch. The final velocity = the average velocity. To find the final velocity, we need to find the toy car's velocity halfway through its journey, as this will equal its average velocity.

As the toy car continues accelerating at the same rate, its final velocity will be twice its average velocity. We can then use this value in our acceleration equation. You MUST remember that to find the final velocity, you must double the average velocity; this will not be on your equation sheet.

Light Gate Version:

• Set up your equipment as shown above, holding the trolley in place, with a string attached to the front that hangs over the edge of the table and over a pulley, with masses attached to apply the force to move the trolley.

• Attach a card to the top of the trolley, and measure its length, plugging this data into the computer

• Measure the distance between the two light gates and plug this data into the computer. The light gates record both the time it takes for the trolley to pass through them (as it records the time that the light beam is broken for) and the time for the trolley to pass between the two light gates.

• When you release the trolley, the computer calculates the initial velocity and final velocity of the trolley at each light gate using the equation, . It then calculates the trolley's acceleration between the two light gates using its change in velocity and the time of travel.

• Repeat the steps above, changing the masses attached to the pulley each time, thus changing the force applied to the trolley, but ensuring to add the removed masses to the top of the trolley so that the total mass of the system remains constant.

Results

Plotting a graph of our results of force against acceleration, and drawing a line of best fit through our results, gives us a graph similar to the one below. The line of best fit passes straight through the origin, showing that force and acceleration are directly proportional, .

To see how mass affects acceleration, again, we could use a stopwatch or light gates. Here, we are going to use light gates because they reduce human error caused by starting and stopping the stopwatch.

• Set up your equipment as shown above, holding the trolley in place, with a string attached to the front that hangs over the edge of the table and over a pulley, with masses attached to apply a constant force.

• Attach a card to the top of the trolley, and measure its length, plugging this data into the computer

• Measure the distance between the two light gates and plug this data into the computer.

• The light gates record both the time it takes for the trolley to pass through them and the time for the trolley to pass between the two light gates.

• When you release the trolley, the computer calculates the initial velocity and final velocity of the trolley at each light gate using the equation, . It then calculates the trolley's acceleration between the two light gates using the change in its velocity and the time of travel between them.

• Repeat the steps above, changing the total mass of the system by adding masses to the trolley, using the computer and light gates to calculate the acceleration of the trolley for different masses.

Results

When a graph of mass against acceleration is plotted from our results, we get a graph like the one shown below. The curve shows that as the trolley's mass increases, its acceleration decreases. Mass and acceleration are inversely proportional.

Improving Your Results

• Friction opposes the motion of the trolley, so using an air track will reduce the friction to almost zero, making the results more accurate.