A cart of mass m = 1.10 kg on a track undergoes a collision with another cart. It's velocity before and after the collision, vi and vf is measured and found to be vi = 2.12¡À0.06 m/s and vf = 0.60¡À0.08 m/s. Calculate the following quantities including their uncertainty. Uncertainties must be stated to correct number of sigfigs, WebAssign will check your answer for the correct number of significant figures. but you should keep more figures for intermediate calculations, rounding only at the end.

To find the quantities including their uncertainties, we can use the principles of uncertainty propagation. Uncertainty propagation involves considering the uncertainties in the initial and final velocities to determine the uncertainties in the calculated quantities.

Let's start by calculating the change in velocity (∆v) and its uncertainty (∆∆v).

∆v = vf - vi = 0.60 m/s - 2.12 m/s = -1.52 m/s

∆∆v = ∆vf + ∆vi = 0.08 m/s + 0.06 m/s = 0.14 m/s

Next, we can calculate the momentum before and after the collision, taking into account their uncertainties.

Initial momentum (pi) = m * vi

Using the given mass (m = 1.10 kg) and initial velocity (vi = 2.12 m/s):

pi = (1.10 kg) * (2.12 m/s) = 2.332 kg·m/s

Final momentum (pf) = m * vf

Using the given mass (m = 1.10 kg) and final velocity (vf = 0.60 m/s):

pf = (1.10 kg) * (0.60 m/s) = 0.660 kg·m/s

Now, let's calculate the change in momentum (∆p) and its uncertainty (∆∆p).

∆p = pf - pi = 0.660 kg·m/s - 2.332 kg·m/s = -1.672 kg·m/s

∆∆p = ∆pf + ∆pi = (0.08 kg·m/s) + (0.06 kg·m/s) = 0.14 kg·m/s

Finally, we can calculate the impulse (∆p) and its uncertainty (∆∆p) experienced during the collision.

Impulse (∆p) = -1 * ∆p = -1 * (-1.672 kg·m/s) = 1.672 kg·m/s

∆∆p = ∆∆p = 0.14 kg·m/s

Therefore, the calculated quantities including their uncertainties are as follows:

Change in velocity (∆v): -1.52 ± 0.14 m/s
Initial momentum (pi): 2.332 kg·m/s ± 0.026 kg·m/s
Final momentum (pf): 0.660 kg·m/s ± 0.14 kg·m/s
Change in momentum (∆p): -1.672 kg·m/s ± 0.14 kg·m/s
Impulse (∆p): 1.672 kg·m/s ± 0.14 kg·m/s

Note: The uncertainties are carried to 2 decimal places since they are the largest uncertainties given.