We will use this slow-motion video (Text description of Direct Measurement Video) to explore how and when we can apply conservation of linear momentum and conservation of kinetic energy to collisions. Our objective is to analyze a concrete example of how forces within a system affect conservation of kinetic energy and linear momentum during a collision. Specifically, we will:Define a specific system that is most useful for our analysis. Use the concepts of impulse and work to explore why internal friction forces affect the kinetic energy of a system, but not the linear momentum of the system. The event we will analyze is a heavy iron weight-lifting disk coming into contact with a rolling low-friction cart after it is dropped vertically onto the cart. After bouncing and sliding across the cart's surface, the disk comes to rest with respect to the cart's surface, and the disk and cart move together. To simplify and clarify this analysis, we'll consider the horizontal motion only. Would you predict that linear momentum and/or kinetic energy are conserved during this collision? Knowing when and how to apply the conservation laws for these two quantities is an important part of analyzing interactions between objects. Let's do some analysis of this interesting situation to see whether and why linear momentum and kinetic energy are conserved or not conserved.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft

the speed of the cart after 3 seconds of low fan speed is ⇒ 54.0 cm/s.

the speed of the cart after 5 seconds of medium fan speed is ⇒ 120.0 cm/s.

the speed of the cart after 2 seconds of high fan speed is ⇒ 64.0 cm/s. 

just did the lab.