AP Test Problems: Solutions and Checks for Fatty Packet Questions

[aceXstudent]

I have some questions (or checks) on some problems from a fatty packet our teacher decided to give us for the AP test. If I've already given a possible solution, see if I did it right. Thanks!



Problem 1:

A simple pendulum consists of a mass 1.8kg attached to a string of length 2.3m hanging off a ceiling. A light horizontal string attached to a wall holds the pendulum at an angle of 30* from the vertical.

(a) Draw a free-body diagram.

Tension 1 (T.) - 60* (+y)
Tension 2 (T,) - 0* (+x)
Weight (mg) - 90* (-y)

(b) Calculate the tension in the horizontal string.

Since [T,=T.x], find [T.x] by using trigonometry after finding that [T.y=mg].

(c) The horizontal string is now cut close to the mass, and the pendulum swings. Calculate the speed of the mass at the lowest position.

Here's where I forget what to do. Do I find the period? Then what do I have to do?

Problem 2:

A ball attached to a string of length [L] swings in a horizontal circle with constant speed. The string makes an angle [A] with the vertical, and [T] is the tension. Express your answer with these terms and fundamental constants.

(a) Draw free body diagram.

Tension (T) - A (+y)
Weight (mg) - mg (-y)

(b) Determine the mass of the ball.

Do I use [2(pie)(square root of (l/g))=2(pie)(square root of (m/k))]?

(c) Determine the speed of the ball.

Like the simple pendulum above, I have no idea.

(d) Determine the frequency of the ball.

Since [T=1/f], do I use one of the period equations from part (b)?



This is it (for now). Once again, thanks for your time.

 

[Andrew Mason]

I have some questions (or checks) on some problems from a fatty packet our teacher decided to give us for the AP test. If I've already given a possible solution, see if I did it right. Thanks!

Problem 1:

A simple pendulum consists of a mass 1.8kg attached to a string of length 2.3m hanging off a ceiling. A light horizontal string attached to a wall holds the pendulum at an angle of 30* from the vertical.

(a) Draw a free-body diagram.

Tension 1 (T.) - 60* (+y)
Tension 2 (T,) - 0* (+x)
Weight (mg) - 90* (-y)

I am not sure what you mean here.

(1) $$T_1sin30 = T_2$$

and:

(2) $$T_1cos30 = mg$$

(b) Calculate the tension in the horizontal string.

Since [T,=T.x], find [T.x] by using trigonometry after finding that [T.y=mg].

Your nomenclature is a little unconventional, but you may have the right idea. Just solve (1) above for T2

(c) The horizontal string is now cut close to the mass, and the pendulum swings. Calculate the speed of the mass at the lowest position.

Just use energy: what is the potential energy just before it is cut? What is the potential energy at the bottom? How does the kinetic energy of the mass relate to the difference in potential energy? Work out the speed from that.

Problem 2:

A ball attached to a string of length [L] swings in a horizontal circle with constant speed. The string makes an angle [A] with the vertical, and [T] is the tension. Express your answer with these terms and fundamental constants.

(a) Draw free body diagram.

Tension (T) - A (+y)
Weight (mg) - mg (-y)

(b) Determine the mass of the ball.

Do I use [2(pie)(square root of (l/g))=2(pie)(square root of (m/k))]?

Use centripetal force: $TcosA = F_c$ and $TsinA = mg$

(c) Determine the speed of the ball.

How do you determine the speed from the centripetal force and radius? What is the radius?

(d) Determine the frequency of the ball.

Since [T=1/f], do I use one of the period equations from part (b)?

Determine the angular speed, $\omega$ from the speed, v and radius.

AM

 

[aceXstudent]

New Questions

Sorry to bother, but I have some more questions. Thanks for the tips and hints for my last questions.

Problem:

A large rectangular raft with a density of 650 kg/m^3, a surface area of 8.2m^2 at the top, and a volume of 1.8m^3 is floating on lake water with a density of 1000kg/m^3.

(a) Calculate the magnitude of the buoyant force on the raft and state its direction.

I used [F=pVg], but I'm pretty sure that answer was wrong.

(b) If the average mass of a person is 75kg, calculate the maximum number of people that the raft can hold before sinking, assuming that the people are evenly distributed on the raft.

I was thinking of deriving an equation with everything calculable, changing the mass unit by 75kg everytime I added a person. I need help on putting the equations together correctly.

 

[DaMastaofFisix]

Mkay, well I can see this is for the B exam. I'm taking the C exam, but I'll see where I can help here. For part a of your second question, it looks like you need readjust your forces equation. Remember, the buoyant force is F=mg, where the m is the mass of the DISPLACED FLUID. So you need to go about figuring out how much fluid is displaced by that raft, which you can find from the densities that are given.

As for the second part, that's where you want to use the straight up fluid force equals the wiehgt of everyone on the raft. because at the point of sinkage, the raft is basically submerged, so the entire volume is under water, therefore letting you use the full pv as a replacement of the m you calulated before.

Hopefully that was a little leg up on the problem. try to work it out and let us know how you did.