## Design Lab Force of Sponge

To determine the force applied by the stationary sponge when a cart at different speeds collides. In this experiment, a cart will collide with a sponge and because of Newton’s third Law of motion, the sponge will apply force on the cart as well, which will push it backwards. The cart will be released using the elastic force from a rubber band. This rubber band will be set as a slingshot where the cart will be placed between it.

A photogate will be placed almost halfway between the slingshot and the sponge that will record the time for the cart. This will further give us the instantaneous velocity of the cart. After the cart collides with the sponge, the cart moves a certain distance backwards which can be measured using a meter stick (measured from the end point of the sponge to front most point of the cart). Using a stopwatch the time, that the cart takes to come to rest after collision, can be measured. As we have the distance covered and the time, the average velocity of the car can be determined using the formula [v = d / t].

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 = F?t = m?v Hence, F= (m?v) / 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 1. Cart 2. Sponge 3. Photogate (0.001s) 4. Rubber band 5. Meter stick (0.001m) Procedure 1) Set up the sponge against a wall such that it remains stationary. (use tape if necessary) 2) Set the cart at least 1 meter away from the sponge and set it within a rubber band, like a slingshot. 3) Place a photogate at almost halfway through and mark the point where it is placed 4) Make sure that a meter stick is placed parallel to the apparatus with its tip at the end point of the sponge.

5) Now release the slingshot such the cart collides with the sponge and moves a certain distance backwards 6) As soon as the cart hits the sponge, start a stopwatch and stop when the cart comes to rest. Record this time. 7) Also, note down the distance of the cart when it moves backwards 8) Repeat steps 2, 5 and 6, where the slingshot is stretched more each time such that the velocity of the cart increases. 9) 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.