Practice Makes Perfect III

36 Practice Makes Perfect III

More practice!

Exercise 36.1: Mighty Kacy

In the show American Ninja Warrior, Kacy Catanzaro was the first woman to complete the full obstacle course. This included the climb shown below.

Kacy is short and petite. Let’s assume a mass of about 100 lb, or 50 kg. Also, rubber has frictional coefficient comparable to that of the palm of our hand, $\mu_s\approx 0.6.$ Assume Kacy pushes equally hard into the wall with her arms and legs. Find the normal force of the wall pushing on Kacey.

Exercises 36.2: Snatchblock!

Consider the setup below. The hanging mass is $M$ , the mass on the table is $m$ , and the frictional coefficient between the box and the table is $\mu$ . The hanging mass starts a height $h$ from the floor. (Only use the slider below if you get stuck on part B).

A. If the box on the table moves a distance $d$ , how much will the hanging mass move? Use your answer to find how the acceleration of the mass on the table compares to the acceleration of the hanging mass.

B. How fast will the hanging mass be moving when the hanging mass hits the floor?

Exercise 36.3: An Accelerating Rocket Ship

A rocket ship in outer space is initially at rest. At $t=0$ , you start the engines at full blast, then slowly ramp down the engines. The acceleration of the rocket for $t\geq 0$ is described by the following equation:

$\vec a(t) = a_0 e^{-t/\tau}\hat x$

where $a_0>0$ is a constant.

A. After a long time ( $t\gg \tau$ ) has passed, will the rocket by accelerating, and if so, in which direction? Justify your answer in English.

B. After a long time ( $t\gg \tau$ ) has passed, will the rocket be moving, and if so, in which direction? Justify your answer in English. Find a reasonable guess for an expression for the final velocity of the particle without doing any math. (Hint: use units!).

C. After a long time ( $t\gg \tau$ ) has passed, will the rocket end to the right or to the left of its initial position? Justify your answer in English.

D. Find $\vec v(t)$ , the velocity of rocket as a function of time, and the position of the rocet as a function of time. Are your final expression consistent with your answers for parts A through C?

I want to point out an important feature of the last problem. You will notice that parts A through C of the problem were really about thinking about what’s going on in English to get some idea on our head of what is happening with the rocket. Then, when we do the math in part D, we can check whether our answer agrees with our expectations. This is extremely powerful: it is easy to make algebra mistakes, so you can double check your math simply by trying to reason out whether your answer makes sense. If it doesn’t, chances are you screwed up the algebra somewhere.

36 Practice Makes Perfect III

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