Question

physics lab
A device is created in the lab which measures the velocity of two carts on a track. The two carts are proving towards each other. Cart A is moving the right and Cart B is moving to the left. After an inelastic collision they are moving, stuck together, to the right. Momentum is conserved in this experiment. The equation relating the momentum to the mass and velocity is: p = mv where p is the momentum, m is the mass, and v is the velocity. The following table contains the data as measured in the experiment: Find the initial momentum, p, of Cart A. Be sure to include the combined uncertainty. P = mv 2 rightarrow p (253 - 3) (0.87) = 220.4 combined uncertainty = (253.3) 2+(0.87) 2+(220.4)2 Find the initial momentum, p, of Cart A. Be sure to include the combined uncertainty. Calculate the final momentum(p) and the final velocity(p) of the carts. Be sure to mdude W\e combined uncertainty. A digital meter and an analong meter Were Used t0 measure two quantities. The digital meter measured the time it takes for a ball to travel between two points. The analog meter measured the distance between two points. The following readings were shown on the displays. (Note that the arrow marks the endpoint location of the distance measurement.) State what pdf (probability density function) you would use to calculate the uncertainty for the time measured for the ball. Use the pdf you chose in part (a) to calculate the uncertainty for the time measured. You must show all work to receive full credit.

Answer 1

question 1) you have to convert the mass to kg

Combined uncertainty :

$u = \sqrt{u_m^2 + u_v^2} = \sqrt{(0.05\times10^{-3})^2 + (0.02)^2} = 0.02$

question 2) same procedure:

and the uncertainty is the same.

Question 3) Conservation of linear momentum

Momentum for B is negative , because it's moving to the left.

Solving for final velocity you get:

The combined uncertainty is for this expression:

$v_f = \frac{p_A+p_B}{m_A+m_B}$

The uncertainty for the numerator is:

$u_1 = \sqrt{u_{p_A}^2 + u_{p_B}^2} = \sqrt{(0.02)^2+(0.02)^2} = 0.028$

and for the denominator:

$u_2 = \sqrt{u_{m_A}^2 + u_{m_B}^2} = \sqrt{(0.05\times10^{-3})^2+(0.05\times10^{-3})^2} = 7.1\times10^{-5}$

The uncertainty for the quotient is:

$u = \sqrt{u_{1}^2 + u_{2}^2} = \sqrt{(0.028)^2+(7.1\times10^{-5})^2} = 0.028$