Momentum plays a key role in this investigation. The law of conservation of momentum states that in the absence of net force, the momentum before collision is equal to the momentum after collision. This means that the momentum of the cart before collision is equal to the momentum after collision. This leads us to the formula:
(mcartvcart)before = (mcartvcart)after
Also, from the formula of impulse, it can be determined that:
Impulse = FΔt = mΔv
Hence, F= (mΔv) / t
Because we have already recorded the time that the cart takes to come to rest after collision, we can put it in the above formula, along with the momentum calculated before. This will finally give us the force exerted.
Independent variable: Speed of the cart
Dependant variable: Force applied by the sponge, Distance covered by cart after collision.
Controlled variable:
Type and size of sponge: As more mass or size of sponge affects the force exerted
Mass of cart: More mass means more momentum
Friction of surface: Friction means that there is net force
Shape and size of cart: As there is air resistance, bigger cart has more surface area
Size and type of rubber band: If the thickness of the rubber band is changed, it will apply more force on the cart
Materials Required
- Cart
- Sponge
- Photogate (±0.001s)
- Rubber band
- Meter stick (±0.001m)
Procedure
- Set up the sponge against a wall such that it remains stationary. (use tape if necessary)
- Set the cart at least 1 meter away from the sponge and set it within a rubber band, like a slingshot.
- Place a photogate at almost halfway through and mark the point where it is placed
- Make sure that a meter stick is placed parallel to the apparatus with its tip at the end point of the sponge
- Now release the slingshot such the cart collides with the sponge and moves a certain distance backwards
- As soon as the cart hits the sponge, start a stopwatch and stop when the cart comes to rest. Record this time.
- Also, note down the distance of the cart when it moves backwards
- Repeat steps 2, 5 and 6, where the slingshot is stretched more each time such that the velocity of the cart increases.
- Use the data collected to first calculate the velocity of the cart, then the momentum and then the force using the formula derived from impulse.
The apparatus is set up as below: