Question

I have a lab assignment that I'm not sure how to do. The experiment is a cart moving 60cm distance and there is a fan on top of it making it have a mass of .56kg. Every trial there is 100g added to the cart. For this part, the time is kept the same.

1. If the force provided by the fan was the same for each run and we have chosen the same time interval, how does the impulse from that force compare from one run to another? Make sure that you use the definition of impulse ( J=Favg∆t) in your explanation.

2. Will the change in momentum the same (or nearly the same) for each of the runs?

Extra questions not related to experiment.

1. What do you conclude about the relationship of work and changes in kinetic energy?

2. What do you conclude about the relationship of impulse and changes in momentum?

Answer 1

Given,
In an experiment
cart is moving d = 60 cm distance
there is a fan on top of the cart with mass m1 = 0.56 kg
every trial 100 g is added to cart, but the time is kept same

1. force provided in each run by the fan is the same
and time is the same
now impulse is FdT
so this remains the same for all the runs and will not depend on mass added to the cart
  
2. Since the provided impulse is the same in all cases, the change in momentum will also be the same in all cases because inpulse provided is nothing but change in momnetum. this is restatement of newtons second law in momentum form.

1. in our experiment we can see
impulse FdT = change in momentum d(mv)
so, Fdt = mdv + vdm
since dm is 0.1 kg (mass is increased in each run)
Fdt = 0.1 + mdv
dv = (Fdt - 0.1)/m
so with increasing mass change in velcity of the cart in the time intervzal for the same applied force is smaller

also, work energy relation ship we can conclude from conservation of energy is that
gain in KE of system = loss in potential energy
  
2. for impulse changes and momentum
we can conclude
applied impulse on a body is equal to its momentum change (from conservation of momentum and newtons 2nd law)