How does the height of the ramp affect the velocity of the soup can?
As the height of the ramp increases the velocity at which the soup can goes down increases as well. The velocity can be figured out using either a velocity graph or the equation D= r/t to find the velocity at a certain time but in this lab we will use the distance equation which has been solved for the three runs of the can with different amount of book:
Two books
D=r/t 94=r/2.44 r=94/(2.44) r= 38.525 cm/s |
Three books
D=r/t 94=r/2.28 r= 94/(2.28) r= 41.228 cm/s |
Four books
D=r/t 94=r/1.68 r= 94/(1.68) r= 55.952 cm/s |
Since we now have the velocity values we can see how this affects the potential energy of the carts at the top of the ramp which we could then compare to the kinetic energy values and see if the conservation of energy applies to what we're seeing.
Potential Energy Kinetic Energy
Two books
|
PE=mgh
PE= 0.305(9.8)(0.07) PE= 0.20923 J |
KE= 1/2(m)(v)^2
KE= 1/2(0.305)(.38525)^2 KE= 0.0453 J |
Three books
|
PE=mgh
PE= 0.305(9.8)(0.105) PE= 0.313845 |
KE= 1/2(m)(v)^2
KE= 1/2(0.305)(0.41228)^2 KE= 0.0518J |
Four books
|
PE=mgh
PE= 0.305(9.8)(0.14) PE= 0.41846 |
KE= 1/2(m)(v)^2
KE= 1/2(0.305)(0.55952)^2 KE= 0.0955 J |
Even though the Kinetic energy and potential energy are different for the different book runs it still obeys the conservation of energy law. The Energy that was gained must have been due to the friction, sound, or air resistance of the can. And so to put this into simper terms since there was an increase in height of the ramp there was also more potential energy being converted to Kinetic energy. This means more energy of motion when the can comes down the ramp resulting in a faster velocity.