Part D: Problem Solving in One Dimension

Exercises

Below are three Conservation of Momentum problems. The first one has been

done for you. The next two you must complete.

Question $4$: so here image $3$ is the the thing I$\text{'}$m looking for, like, i want to know what type of collisions are taking place in here in the questions given below

Consider a collision between two carts on a one$-$dimensional track. Initially, one cart

$($with mass $1\mathrm{.}1$ kg$)$ is moving at $0\mathrm{.}65$ m$/$s$,$ while the second cart $($mass $4\mathrm{.}4$ kg$)$ is at rest.

After the collision, the less massive cart moves at $0\mathrm{.}39$ m$/$s in the opposite direction.

Find the velocity of the other cart after the collision.

Solution

P$\_($i$)=$P$\_($f$)$

m$\_(1)$v$\_(1$i$)+$m$\_(2)$v$\_(2$i$)=$m$\_(1)$v$\_(1$f$)+$m$\_(2)$v$\_(2$f$)$

m$\_(1)$v$\_(1$i$)+0=$m$\_(1)$v$\_(1$f$)+$m$\_(2)$v$\_(2$f$)$

v$\_(2$f$)=($m$\_(1)($v$\_(1$i$)-$v$\_(1$f$)))/($m$\_(2))$

v$\_(2$f$)=0\mathrm{.}26($m$)/($s$)$

Problem$-$Solving Hints

Sketch the before and after motion of

the objects to help you to picture the

collision and determine velocity signs.

Make a list of known quantities. Here,

V$\_(2$f$)$ is the unknown in question.

Write the general equation to be used.

Here, Conservation of Momentum will

provide the solution to this problem.

This equation is rewritten using the

variables in this problem.

Solve for the unknown, then substitute

to find the numerical solution. Be sure to

include the proper units and round to the

correct number of significant digits. For the type of collilsoin $55,200$ kg $14\mathrm{.}3$ m$/$s$,$ while the other boxcar

moves at $10\mathrm{.}4$ m$/$s in the same direction. After the collision, the two boxcars are coupled

and move together at $11\mathrm{.}8($m$)/($s$).$ Find the mass of the other boxcar.

Question $6$

Cannons in the past were often mounted on rails such that they rolled backwards when

fired, as shown below. Consider a $1300$ kg cannon firing a $72$ kg cannonball. When

fired, the cannonball travels at $55$ m$/$s$.$ Find the velocity of the cannon.

State whether each of the following interactions is explosive, elastic, inelastic, or

perfectly inelastic. Give supporting calculations and$/$or explanations. a$)$ Activity $8\mathrm{.}1$

Question $4,$ b$)$ Activity $8\mathrm{.}1$ Question $5,$ and c$)$ Activity $8\mathrm{.}1$ Question $6.$