5[E]) You\'ve just bought a framed, vintage 43 in by 30 in poster of your favori

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5[E]) You've just bought a framed, vintage 43 in by 30 in poster of your favorite movie. The frame has two hooks on the upper-left and upper-right corners and you have two thin, 3 foot wires that you want to use to hang the poster. You intend to attach the wires to some hooks that you'll position near your ceiling so that the wires hang straight down while holding up the poster. Each of these wires supports up to 170 pounds and your poster and the frame together weigh about 40 pounds. How much weight is being supported by each wire?

6[M]) You feel like the poster is hanging too low and decide you'd like to spread the ceiling hooks out so that it hangs higher up. What's the maximum distance you can spread the ceiling hooks out while keeping the poster level?

7[M]) You watch two figure skaters as they gracefully dance on the ice. At one point during their routine they come to a stop and the woman pushes her partner away. It takes her a second to complete the motion, during which time her partner moves about 1 foot away from his original location. After the push, her partner drifts an additional 6 feet while she appears to drift in the opposite direction about 2 times as fast as he does. They drift apart for 3 seconds, and then the male figure skater stops himself and proceeds to skate back to his partner. After an elegant double-twirl, they end with a bow. You wonder how hard the female figure skater pushed her partner. You do a little internet research and discover that she is 5 feet tall and about 40 kg.

8[M]) As a follow-up question, you wonder how much the male skater weighed. You would like to figure it out from your observations rather than look it up.

9[E]) You're standing on an elevator as it starts to move. You're surprised by the rate at which the elevator speeds up, so you decide to skip your floor and see for yourself. You take out your smartphone and start up a free app that displays its accelerometer readings. You place the phone on the floor. As the elevator starts to move again, the phone indicates that the elevator's acceleration has gone up by about 2.50 m/s^2. The phone is about a quarter of a kilogram. What's the normal force on the phone?

10[E]) What does the elevator's acceleration need to be in order for the normal force on you to be zero? (let positive numbers point up along the vertical and negative numbers point down).

11[M]) While driving in the mountains, you notice that when the freeway goes steeply down hill, there are emergency exits every few miles. These emergency exits are straight dirt ramps which leave the freeway and are sloped uphill. They are designed to stop trucks and cars that lose their breaks on the downhill stretches of the freeway even if the road is covered in ice. You are curious, so you stop at the next emergency road. You estimate that the road rises at an angle of 20 degrees from the horizontal and is about 150 yards long. You wonder what's the fastest a car could be travelling and still come to a stop on the emergency ramps, even in the worst possible conditions.

12[E]) You and a friend are driving to Not Your Average Joe's to celebrate the end of finals with some other friends. Your friend is driving and makes a turn around a 90 degree bend, maintaining a constant speed of about 30 mph. You slip sideways on your seat (whoops---you forgot to put on your seatbelt!), and feel like you're pushed into the door. What force is primarily responsible for keeping you inside the car (use 'G' for gravitational, 'T' for tension, 'F' for friction, and 'N' for normal)?

13[M]) The turn takes about 1 seconds. Estimate how strong the force is keeping you in the car. You can assume your mass is about 100 kg for the purposes of this estimate.

14[M]) You're taking a ride in a cab, and you notice that the fuzzy dice that the driver keeps hanging from the rearview mirror are tilting out at an angle of about 15 degrees from the vertical. Since you can't see the dashboard, but you're curious about the acceleration of the cab, you decide to figure it out based on your observations. You assume that the ground the cab is driving on is approximately level.

15[H]) You're playing with your father's brother's nephew's cousin's former roommate's niece. She wants you to push her around in her go-cart. You notice a rope attached to the front of the cart and figure that it would be easier to pull her rather than to push her. You estimate that she weighs about 40 pounds, the go-cart weighs about 20 pounds and that the rolling friction on the ground behaves similarly to a 0.10 coeffient of kinetic friction. You want to figure out the angle above the horizontal at which to pull her that will involve the least effort from you.

16[M]) How much more force would you have had to exert (at minimum) to push her rather than pulling her? Assume that your push as angled downward at about 20 degrees below the horizontal.

17[E]) You are driving a flatbed truck carrying a couple of planks of wood on the bed at the rear of the truck. While driving on the highway, you realize that you forgot to secure the planks, so they are at risk of falling off the back of the truck. You want to get to an exit as quickly as you can, but you need to ensure that the planks won't slide off the truck. You happen to recall that the coefficient of friction between pieces of wood is about 0.25, but you can't remember if this corresponds to static or kinetic friction! Nevertheless, you realize that this will at least be useful for allowing you to estimate a safe acceleration for your car. Why can you be so confident? (type "A" if its because static friction coefficients are usually bigger than those for kinetic friction, "B" if its because kinetic friction coefficients are usually bigger than those for static friction, "C" if the static and kinetic friction coefficients are usually about the same, or "D" because static and kinetic friction coefficients don't matter if the objects weigh enough).

18[M]) What's is the acceleration you estimate based on your considerations?

19[M]) Oh no! You start to accelerate at the rate you estimated but both of the planks begin to slide. You start to lower your acceleration and the planks stop sliding. Then you inch the acceleration up to until it's about 0.98 m/s^2, which is where the planks just start to slide again. So, you lower your rate of acceleration a little bit below that and are able to accelerate without worrying about the slippage of the planks. What's the coefficient of static friction between the bed of your truck and the wooden planks?

20[M]) Suppose you need to turn to make the next exit. You're going to need to make it pretty tight, about 20 feet in radius. What's the maximum speed you can maintain during the turn while avoiding making the planks slide around the truck's bed?

21[H]) You landed a great summer internship as the assistant to Christopher Nolan's technical director for the upcoming Batman movie. During one sequence, Mr. Freeze has managed to knock Batman off of the front of a train. He's also frozen the front face of the train solid, so Batman has no grip on the train and is about to start sliding down. In the midst of this action, Robin has successfully taken control of the train and quickly realizes that he must do something to rescue Batman. The script calls for Robin to accelerate the train so that Batman can keep from slipping and have time to gain a foothold in the ice. The technical director has asked you to find out if the stunt is feasible by working out the necessary acceleration magnitude for the train (realistically, the train can only accelerate at a maximum of about 0.5 m/s^2). The front of the train is sloped at 45 degrees from the horizontal.

22[H]) Nolan decides to alter the script so that Robin maxes out the train's acceleration, but it's not enough to keep Batman from sliding. However, Batman's costume is equipped with little spikes that he is able to stick into the ice, effectively creating a friction effect. The costume designers need to know how to set up the spikes so that the coefficient of friction is just high enough to keep Batman from slipping relative to the train. The technical director assigns you the task of figuring this out.

Explanation / Answer

5) 20lbf

6) ?

7) 48.77N

8) 784.00N

9) ?

10) -9.8m/s^2

11) ?

12) N

13) use the equation (mv^2)/r however, you need to solve for r using (4tv)/2pi

14) ?

15) ?

16) ?

17) A

18) 2.45m/s^2

19) 0.099

20) 2.44m/s

21) 9.8m/s^2

22) ?

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