Suppose that the force is applied perpendicular to the torque arm. Given: $\tau=35.7\ \mathrm{lb}\ \mathrm{ft}$ $r=0.0240 \mathrm{ft}$

$$F= ?$$

Consider the region bounded by the graphs of the equations $y=x \sqrt{x+1}$ and y=0.

Find the volume of the solid generated by revolving the region about the y-axis.

If you leave me refrigerator door open and the refrigerator runs continuously, does the kitchen get colder or warmer? Explain.

In the earlier example given, was treated the merry-go-round plus child as a system (shown in the given figure) whose angular momentum is conserved. The merry-go-round is initially at rest, so its initial angular momentum is zero, but at the end it is rotating, so its final angular momentum is nonzero. The angular momentum of the merry-go-round alone thus changes, which can only happen if there is a torque on the merry-go-round. What force provides this torque?

(a) The force of gravity on the merry-go-round

(b) The force of air drag on the merry-go-round

(c) The force produced by the child when she jumps off

(d) The force of friction at the axle of the merry-go-round

"Suppose the snark population on Citsigol Island is currently 3,400 and growing at a rate of 18% per year.

a. Write a recursive definition for the sequence $P$ of snark populations $n$ years from now (assuming an unlimited growth model).

b. Write an explicit formula for the population $P$ of snarks $n$ years from now (assuming an unlimited growth model).

c. If the snark population is modeled with the limited growth model difference equation $P_{n+1}=P_n+0.18 P_n\left(1-\frac{P_n}{17000}\right)$, what is the end behavior of the sequence $P$ ? What does the end behavior mean in this situation?"

We all carry 20,000 to 25,000 genes in our genome. So far, patents have been issued for more than 6000 of these genes. Do you think that companies or individuals should be able to patent human genes? Why or why not?

Garage door openers originally had a series of four on/off switches so that homeowners could personalize the frequencies that opened their garage doors. If all garage door openers were set at the same frequency, anyone with a garage door opener could open anyone else's garage door.

3. How many different positions are possible with 8 consecutive on/off switches?

Solve previous problem for the case where the assembly starts from rest with an initial angular acceleration $\alpha=900 \mathrm{rad} / \mathrm{s}^{2}$ as a result of a starting torque (couple) M applied to the shaft in the same sense as N. Neglect the moment of inertia of the shaft about its z-axis and calculate M.

What is the net torque about the axle on the pulley in the figure below? If your net torque is negative; do not forget to add a negative sign in your answer. Remember in our convention, counter-clockwise means positive.

Getting into a car involves these steps. Open the car door. Sit down. Close the door. Buckle the seat belt. Describe the steps you take in getting out of a car. How are they related to the steps involved in getting into a car?

The Stanford linear accelerator can accelerate electrons to kinetic energies of $50 \mathrm{GeV}$. What's the de Broglie wavelength of these electrons? Compare with the diameter of a proton, about $2 \mathrm{fm}$.

Underline the main clause in given sentence. Then circle the subordinate clause.
If the door is open, you can go right into the house.

Explain why you cannot cool your kitchen by leaving your refrigerator door open on a hot day. (Why does turning on a room air conditioner cool down the room, but opening a refrigerator door does not?)

Using conversion factors, solve the following clinical problem: A nurse practitioner prepares 500. mL of an IV of normal saline solution to be delivered at a rate of 80. mL/h. What is the infusion time, in hours, to deliver 500. mL?