Hovercraft B/C

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Justin72835
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Re: Hovercraft B/C

Postby Justin72835 » March 22nd, 2018, 5:40 pm

UTF-8 U+6211 U+662F wrote:Ohh, I see.
Answer


Not really sure since I still haven't quite wrapped my head around rotational stuff.

EDIT: Over-complicated things the first attempt

The LaTeX finally loaded! Also, your revised version is correct so good job; your turn!
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Re: Hovercraft B/C

Postby UTF-8 U+6211 U+662F » March 22nd, 2018, 6:11 pm

Cool (finally!)

A 1 lb point mass is held up by two ideal ropes. One rope is vertical and 55 cm long. The other is at an angle from the vertical rope. It is attached to the same "ceiling" as the other rope, so it looks something like this:

Code: Select all

---------------------
|   /
|  /
| /
|/
O


Imagine you suddenly decrease the length of the rope to the right by half of the length of the rope to the left. Find the tension in each rope (magnitude and direction) after the system reaches static equilibrium if the angle between them was originally
a) as close to 0 degrees as possible
b) 30 degrees
c) 45 degrees
d) 60 degrees
e) as close to 90 degrees as possible

EDIT: Unfortunately, I made an error when I first did this problem, and the algebra is more complicated than I thought (meaning very time-consuming). Thus, I will ask another problem :/

Three masses are held up to a ceiling by three ropes, like so:

Code: Select all

___
 |
 O
 |
 O
 |
 O


The ball on top has a mass of 5 kg, the ball in the middle 3 kg, the ball on the bottom 1 kg. Assuming the ropes are ideal, find the tension in each rope.

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Re: Hovercraft B/C

Postby Justin72835 » March 30th, 2018, 2:55 pm

UTF-8 U+6211 U+662F wrote:Cool (finally!)

A 1 lb point mass is held up by two ideal ropes. One rope is vertical and 55 cm long. The other is at an angle from the vertical rope. It is attached to the same "ceiling" as the other rope, so it looks something like this:

Code: Select all

---------------------
|   /
|  /
| /
|/
O


Imagine you suddenly decrease the length of the rope to the right by half of the length of the rope to the left. Find the tension in each rope (magnitude and direction) after the system reaches static equilibrium if the angle between them was originally
a) as close to 0 degrees as possible
b) 30 degrees
c) 45 degrees
d) 60 degrees
e) as close to 90 degrees as possible

EDIT: Unfortunately, I made an error when I first did this problem, and the algebra is more complicated than I thought (meaning very time-consuming). Thus, I will ask another problem :/

Three masses are held up to a ceiling by three ropes, like so:

Code: Select all

___
 |
 O
 |
 O
 |
 O


The ball on top has a mass of 5 kg, the ball in the middle 3 kg, the ball on the bottom 1 kg. Assuming the ropes are ideal, find the tension in each rope.

Answer
Going from top to bottom, the tensions are as follows:







Essentially, the tension in each rope is equal to the weight that it holds up.
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But in ourselves, that we are underlings."


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Re: Hovercraft B/C

Postby UTF-8 U+6211 U+662F » March 30th, 2018, 2:56 pm

Yep, your turn

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Re: Hovercraft B/C

Postby Justin72835 » March 30th, 2018, 3:02 pm

UTF-8 U+6211 U+662F wrote:Yep, your turn

Your hovercraft device has a mass of 2.25 kg and at max power can travel a speed of 0.2 m/s. You also learn that the target distance is 180 cm and you are trying to get there in 15 seconds.

How many rolls of pennies should you place on the hovercraft in order to get as close to 15 seconds as possible?
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But in ourselves, that we are underlings."


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Re: Hovercraft B/C

Postby MattChina » March 30th, 2018, 3:14 pm

Justin72835 wrote:
UTF-8 U+6211 U+662F wrote:Yep, your turn

Your hovercraft device has a mass of 2.25 kg and at max power can travel a speed of 0.2 m/s. You also learn that the target distance is 180 cm and you are trying to get there in 15 seconds.

How many rolls of pennies should you place on the hovercraft in order to get as close to 15 seconds as possible?


answer
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Re: Hovercraft B/C

Postby UTF-8 U+6211 U+662F » March 30th, 2018, 3:19 pm

Justin72835 wrote:
UTF-8 U+6211 U+662F wrote:Yep, your turn

Your hovercraft device has a mass of 2.25 kg and at max power can travel a speed of 0.2 m/s. You also learn that the target distance is 180 cm and you are trying to get there in 15 seconds.

How many rolls of pennies should you place on the hovercraft in order to get as close to 15 seconds as possible?

Answer
Assuming there is no change in lift (which affects friction) and the hovercraft gets to max speed instantly:
One penny roll is around the mass of 50 (new) pennies, 50 * 3.11 g or 0.156 kg.
Required speed is 1.8 m / 15 s = 0.12 m/s.
(2.25 kg)(0.2 m/s) = (2.25 kg + n * 0.156 kg)(0.12 m/s)
n = 9.6

10

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Re: Hovercraft B/C

Postby Justin72835 » March 30th, 2018, 5:38 pm

UTF-8 U+6211 U+662F wrote:
Justin72835 wrote:
UTF-8 U+6211 U+662F wrote:Yep, your turn

Your hovercraft device has a mass of 2.25 kg and at max power can travel a speed of 0.2 m/s. You also learn that the target distance is 180 cm and you are trying to get there in 15 seconds.

How many rolls of pennies should you place on the hovercraft in order to get as close to 15 seconds as possible?

Answer
Assuming there is no change in lift (which affects friction) and the hovercraft gets to max speed instantly:
One penny roll is around the mass of 50 (new) pennies, 50 * 3.11 g or 0.156 kg.
Required speed is 1.8 m / 15 s = 0.12 m/s.
(2.25 kg)(0.2 m/s) = (2.25 kg + n * 0.156 kg)(0.12 m/s)
n = 9.6

10

Oh sorry, I forgot to mention that you should assume that each roll of pennies has a mass of 125 grams (it's mentioned in the rules manual). However, your answer is technically correct, so you can go ahead with the next one!
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But in ourselves, that we are underlings."


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Re: Hovercraft B/C

Postby UTF-8 U+6211 U+662F » March 31st, 2018, 6:16 pm

Derive the formula for the distance a projectile travels given the angle of elevation of its launch, theta, and the initial speed, v. Assume the projectile encounters no air resistance and starts at ground level.

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Re: Hovercraft B/C

Postby Nydauron » April 1st, 2018, 10:44 am

UTF-8 U+6211 U+662F wrote:Derive the formula for the distance a projectile travels given the angle of elevation of its launch, theta, and the initial speed, v. Assume the projectile encounters no air resistance and starts at ground level.


Answer
First, find the individual components of the 2D velocity vector:




The amount of time the ball will be in the air can be found using



Since and :





To then get the total distance traveled, we simply use .



is the final equation.
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Re: Hovercraft B/C

Postby UTF-8 U+6211 U+662F » April 1st, 2018, 11:18 am

Nydauron wrote:
UTF-8 U+6211 U+662F wrote:Derive the formula for the distance a projectile travels given the angle of elevation of its launch, theta, and the initial speed, v. Assume the projectile encounters no air resistance and starts at ground level.


Answer
First, find the individual components of the 2D velocity vector:




The amount of time the ball will be in the air can be found using



Since and :





To then get the total distance traveled, we simply use .



is the final equation.

Yep, your turn :)

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Re: Hovercraft B/C

Postby Nydauron » April 2nd, 2018, 8:24 am

There is a 20kg ball heading east at 26m/s. A 36kg ball is traveling southwest at 38m/s. If both balls undergo an inelastic collision, what is the speed and the direction of the balls after the collision?
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Re: Hovercraft B/C

Postby UTF-8 U+6211 U+662F » April 2nd, 2018, 6:30 pm

Nydauron wrote:There is a 20kg ball heading east at 26m/s. A 36kg ball is traveling southwest at 38m/s. If both balls undergo an inelastic collision, what is the speed and the direction of the balls after the collision?

Answer
It doesn't seem like there's enough information given to solve the problem, but given that the balls "stick together", then
where east is positive.

or

where south is positive.

or






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Re: Hovercraft B/C

Postby Nydauron » April 2nd, 2018, 8:31 pm

UTF-8 U+6211 U+662F wrote:
Nydauron wrote:There is a 20kg ball heading east at 26m/s. A 36kg ball is traveling southwest at 38m/s. If both balls undergo an inelastic collision, what is the speed and the direction of the balls after the collision?

Answer
It doesn't seem like there's enough information given to solve the problem, but given that the balls "stick together", then
where east is positive.

or

where south is positive.

or







That’s correct. You turn!
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Re: Hovercraft B/C

Postby photolithoautotroph » April 9th, 2018, 5:20 pm

Questions:
1. A uniform disk is rolled down a hill of height 11m. What is the speed of the disk when it reaches the bottom of the hill?
2. As soon as the disk reaches the bottom of the hill, it hits a horizontal surface of frictional coefficient 0.13. What is the acceleration of the disk?
3. A ball of mass 2kg is attached to a string of length 0.75m and rotated vertically with an angular velocity of 7rad/s. What is the ratio of the string tension at the top of the loop to the string tension at the bottom?
Ignore significant figures.
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