# (Physics - Easy) Uniform Circular Motion in a Vertical Circle

A passenger is riding on a Ferris wheel. The seat is fixed in an upright position and does not rotate. If the passenger weights 60 kg, the Ferris wheel travels at a constant velocity of 10 m/s and has a radius of 20 meters, what is the normal force exerted on the passenger at the top and the bottom?

# (Mechanics - Medium) Joint Pains

A friend is designing a bridge and has asked for you help in determining the internal forces of their bridge.

Assuming the bridge is in static equilibrium, find the forces and reaction forces in the members of the truss that are contacting joints A & D. Determine whether those members are in tension or compression.

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Last week we looked at node voltage analysis, also known as nodal analysis, where the circuit was powered only by current sources. When you add a voltage source into the mix, it becomes a dependent variable in your equations.

## Review

When applying nodal analysis, each node tied to a voltage source is dependent on the voltage source, i.e. $v_a=v_S$. When writing your system of equations, this dependency is substituted throughout.

Given resistors R1=2$\Omega$, R2=2$\Omega$, R3=4$\Omega$, R4=3$\Omega$,
current source I=2A, and voltage source V=3V.

What is the current $i$ through voltage source V?

# (Physics - Medium) Minimum Tugging Angle

After an exciting day of fishing, you (A) and your friend (C) are tugging your catches of the day (B) back to camp.

You and your friend exert a net 5000-lb force along the axis of the barge.
So what's the angle, α for which the tension in rope 2 is minimum value?

A) 30°
B) 35°
C) 60°
D) 90°

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# (Calculus - Easy) Passionately Maxin' Profit

During a family reunion dinner, a relative of yours asks you for some advice:

"You're a calculatin' smartie, so I've got a question for you. One of the crops on my farm is passion fruit, and I want to maximize my profit. The crops just starting to get ripe. If I pick some now, I'll get 6,000 passion fruits, which I can sell for a profit of $\$1.50 $each. BUT, for each additional week I delay, we'll harvest about 1100 more when we actually go pick 'em. The only thing is that two things will happen: 1) the profit per fruit will drop about$ \$0.15$ more and 2) 100 of them will be spoiled for each additional week we wait.

Can you help me figure out which week might be the best time to pick my delicious passion fruits?"

• Now!
• 2 weeks
• 4 weeks
• 5 weeks
• PASSION FRUIT?? MY FAVORITE...!!!
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