PPOTW
Physics Problem of the Week! (2 weeks??)
Take a look at the posted problem for the week, and create a solution with proof of your answer. Create a Google Doc that shows how to get the answer, and share it with cmurray@ttsd.k12.or.us. Either solve it on paper and put pictures of your solution in your Doc, or use the formula editor to make it nice. If you solve it graphically, put in screen shots of the graph. Correct solutions (explained, complete) will win the coveted PPOTW prize!!
For all of these, if you click on the title, it will take you to a Google Doc that you can make a copy of and that has the explanation on it.
Problem 25: Two Blocks with Friction
(Submit answers by 5/17/2024)
A 3.00 kg block rests on a 5.00 kg block and there is a coefficient of friction of 0.125 between them. The 5.00 kg block rests on a plane with which it has a coefficient of friction of 0.315.
What is the biggest force you can exert horizontally on the 5.00 kg block without the 3.00 kg block slipping?
Suppose we exert a force of 50.0 N on the lower block.
What is the acceleration of the 5.00 kg block?
What is the acceleration of the 3.00 kg block?
In what time does the 3.00 kg block slip 6.00 cm relative to the 5.00 kg block? (assuming it can slip that far without coming off the 5.00 kg block)
What is the actual displacement of the 3.00 kg block during this time?
Hey - Ben Nickle solved this!!!
(Submit answers by 5/17/2024)
A laminar stream of water is flowing at 11.4 liters per minute (about 3 GPM) from a 2.10 cm diameter faucet. As the water falls it picks up speed and the stream narrows. What is the diameter of the stream a quarter of a second (0.250 s) after it leaves the faucet? (Assuming it stays in a stream) How far has the water traveled in this time?
Ben Nickle solved this one too!!!!
Problem 23: Run on a Merry Go Round
(Submit answers by 5/17/2024)
Suppose a 65.0 kg person stands at the edge of an 8.00 m diameter cylindrical merry-go-round turntable that is mounted on frictionless bearings and has a mass of 225 kg . The turntable is at rest initially, but when the person begins running at a speed of 4.50 m/s (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.
Ben Nickle nearly made a mistake on this one, but then he didn't
Problem 22: A Bucket with A Hole
(Submit answers by 5/17/2024)
A cylindrical bucket has a diameter of 28.0 cm and is 46.0 cm tall. It is initially brim full of water, and there is a 5.00 mm diameter hole drilled in the bottom, but it is covered with duct tape. What time will it take the water to reach a depth of 23.0 cm after the duct tape is removed? Numerical methods entirely appropriate.
Ben Nickle solved this two ways. (I solved it one way - haha)
Problem 21: Resistance Cube of DEATH!
(Submit answers by 1/29/2024)
The outline of a cube is made of resistance wire. Each lineal piece is the same length and has a resistance R (including the little connector leads). In terms of R what is the resistance from A to B?
Ben Nickle Solved this thoroughly
Problem 20: Kirchhoff's Madness!
(Submit answers by 1/29/2024)
Find the voltage difference from A to B. Specifically, which point is more positive, A or B?
(If you click on the title of the problem it will take you to a Goooooogle doc that has a better more readable diagram)
Ben Nickle solved this comprehensively
Problem 19: Ball and Circle II
(Submit answers by 1/29/2024)
A 1.12 kg ball of negligible size is moving clockwise on a string in a vertical circle with a radius of 2.00 meters. Because of gravity, the ball speeds up and slows down, going faster at the bottom, and slower at the top. At the position shown the mass is 1.00 m above the ground, and the tension in the string is 67.0 N. Just after it is in the position shown above on one of its revolutions, the string disappears when the ball is 4.00 m above the ground. How far horizontally from where the string disappears does the ball travel before striking the ground?
Ben Nickle solved this creatively!
Problem 18: Accelerated Incline
(Submit answers by 12/15/2023)
There is a coefficient of 0.215 between a block and a 42.0o incline. If the block starts at rest and the whole system is at rest, what time will it take the block to travel 2.00 m down the incline?
If the plane is accelerating as shown to the left at 4.30 m/s/s, and the block starts at rest what time will it take the block to slide 2.00 m down the incline?
Ben Nickle and Chris Murray submitted solutions to this.
(Submit answers by 12/15/2023)
There is a coefficient of friction of 0.113 between the 19.0 kg block and the 17.0o inclined plane. The block is given a push so initially it is sliding down the plane at 3.70 m/s. How far down the plane will the block go before stopping if it is connected as shown to a 23.0 kg block by a string using a frictionless (and massless) pulley?
Ben Nickle solved this three different ways. Enjoy
(Submit answers by 11/6/2023)
Fred and George are playing with air rockets. Their platforms are 80.0 m away from each other on a level field. Fred launches his rocket at George’s platform at an angle of 65.0 degrees above the level, and at a speed of 32.0 m/s. George has a rocket he can launch at any speed, and any angle in the same plane. 2.00 seconds after Fred launches his rocket, what speed and what angle should George launch his rocket to intercept Fred’s incoming rocket? Let’s say George has to hit Fred’s rocket when it has been in the air for 5.00 seconds so there is just one answer. Ignore air friction, use g = 9.81 m/s/s
Hint: This isn’t as difficult as it sounds. The incoming rocket and its interceptor once launched are in a weightless frame of reference. I solved this without even using the acceleration of gravity. (After I found the position and velocity of the incoming rocket at 2.00 s)
Check your answer: AntiMissile.IP (Download to a PC in the back of my room)
Meah Latt and Ben Nickle submitted successful solutions to the Anti Missile!!
(Submit answers by 10/16/2023)
A person drops a rock from the top of a 50.0 m tall cliff. Exactly 1.00 second after releasing the first rock from rest, they propel a second rock straight downwards so that it catches up with the first rock when it is 10.0 m above the ground. Ignore air friction. Use g = 9.81 m/s/s as the acceleration of gravity.
What downward speed do they have to give the second rock?
Nicole Wood and Ben Nickle solved this problem successfully!
(Submit answers by 10/06/2023)
Ron Weasley has a trunk that is 4.00 feet long and 1.50 feet wide and 2.00 feet deep. The side you see in the diagram is the 4.00'x1.50' side. He was careful to pack it homogeneously so that the center of mass of the trunk is the geometric center of the trunk. He starts from rest a distance of 5.00 meters from the barrier, and accelerates toward the barrier between platforms 9 and 10, but he doesn't want to tip over his trunk. What is the minimum time he can reach the barrier without tipping the trunk? Assume the trunk does not slip with respect to the trolley.
Ben Nickle submitted a very explainey solution to this problem!!
Problem 13: The New Gas Formula
(Submit answers by 09/15/2023)
The IB curriculum for 2023-2024 has been changed for incoming Juniors. As I was looking over the new data packet, I encountered a cool new formula that I had never seen before in the gas laws section...
<Click here to continue - I can't insert formulas into this page editor>
Ben Nickle submitted a great solution to this!
(Submit answers by 09/15/2023)
A. The AtmosFEAR can be simplified to be a point mass on the end of a massless rod. If the rod is 10.5 meters long:
i. How fast are you going at the lowest point if you start from rest at the very top?
ii. What is your centripetal acceleration at the bottom, and does this number depend on the length of the rod?
B. Suppose the rod is not massless. If it has half the mass of the bottom part of the ride, and is a uniform rod itself:
i. How fast are you going at the lowest point if you start from rest at the very top?
ii. What is your centripetal acceleration at the bottom, and does this number depend on the length of the rod?
Ben Nickle submitted a suuuper solution to this!
Problem 11: Dopple Dopple Dopple Doppler
(Submit answers by 05/19/2023)
You are driving 113 m/s* behind a car that is going only 83.0 m/s. When you are 100.0 m behind them you honk your 10,000. Hz horn. You hear an echo off the back of their car.
What time does it take you to hear your own echo?
What frequency do they hear? (give me like crazy sig figs like 5 sf)
What frequency do you hear your echo? (crazy 5 sf)
Assume the air is still, and the speed of sound is 343.0 m/s
Ben Nickle made an elegant solution to this using Desmos.
*These are stunt drivers on a closed course.
Problem 10: Buoyancy Simple Harmonic Motion
(Submit answers by 04/28/2023)
A cylindrical rod that is weighted on one end has a mass of 19.0 grams, a length of 42.0 cm, a diameter of 1.20 cm and floats weighted end down in a fluid with 21 cm below the fluid, and 21 cm above the fluid.
What is the density of the fluid?
The rod is pushed down so that 30.0 cm is submerged, and then released. It bobs up and down. Neglecting the viscosity or inertial effects of the fluid,(i.e. Pretend it’s a superfluid) what is the period of its motion? (Hint - this is SHM, but it’s not a spring causing acting as a restoring force, it’s the buoyant force)
What is its maximum velocity?
Ben Nickle submitted a wonderful solution to this!!!
Problem 9: Cats and Bombs and Buckets of Fried Chicken*
(Submit answers by 04/14/2023)
How many cats are in the box with the “?” (Ignore the mass of the structure - the only things that have weight are Cats and Bombs and Buckets of Fried Chicken)
Hint - a balance beam balances when the clockwise torques = the anti clockwise torques
Ethan Hoang, Nicole Wood, and Ben Nickle have submitted correct solutions to this PPOTW!!!!
*I don’t know who created this. I hope they don’t sue me. Cory Peters shared it with me years ago.
(Submit answers by 03/24/2023)
The coefficient of kinetic and static friction is 0.215 between a block “B” and a wall “W”. The wall has a mass of 5.00 kg, and the surprisingly dense block B has a mass of 4.50 kg. Initially, the bottom edge of the block is exactly 3.00 m from the bottom of the wall. The wall is sliding and accelerating to the left such that the block B maintains contact with it because of inertia. The coefficient of friction between the odd sliding wall and the floor is 0.120.
If the wall is accelerating at 24.0 m/s/s to the left, and the block starts sliding down the wall from rest,
What is the acceleration of block B down the wall?
What is the force the block and wall system is exerting on the floor?
What force to the left exerted on the wall would cause this acceleration?
Suppose the same setup, but this time there is a force of 285 N applied to the left on the wall as the wall is sliding to the left.
What is the acceleration of the wall? (give me like 3 decimal places)
What will be the acceleration of block B down the wall?
What force would you have to apply to the left on the wall as it slides left so that the block would take exactly 1.00 seconds to go down the wall?
Ben Nickle has submitted a solution to this!!
(Submit answers by 03/03/2023)
A 7.00 kg mass and a 3.00 kg mass are attached to the same string that is around a massive uniform cylinder that is free to rotate about its center with a diameter 3.80 m and a mass of 14.0 kg. Both masses are 5.00 m above the ground. Initially the system is at rest, but the 7.00 kg mass is released, and accelerates downward, striking the ground. Assume the string does not slip while there is tension in it, and neglect the mass of the string, and any friction of the rotating cylinder.
With what speed does the 7.00 kg mass strike the ground?
What is the linear acceleration of the 7.00 kg mass downward?
What is the greatest height the bottom of the 3.00 kg mass reaches above the ground?
Zion Ocholi and Ben Nickle submitted correct solutions to this - Zion uses conservation of energy, and Ben shows how to do both!
Problem 6: Brennen and the Carts
(Submit answers by 02/17/2023)
60.0 kg Brennen is playing on two flatbed rail cars initially at rest. Car A has a mass of 315. kg and B 462. kg. He reaches a velocity of +6.30 m/s to the right on A, before jumping to B where he slows to +3.10 m/s to the right before jumping off the other end. The cars are uncoupled, and rest on a frictionless track:
What is the velocity of car A when he is in midair?
What is the velocity of car B when he leaves it?
What would have been the velocity of car B had he remained there, and not jumped off?
What would the velocity of car B have been had he jumped off the left side of it to give himself a velocity of zero?
So a mathematician, a physicist and an engineer submit solutions for the Physics Problem of the week...
Three great solutions to this from Meah Latt, Ben Nickle and Zion Ocholi!!!
https://users.cs.northwestern.edu/~riesbeck/mathphyseng.html
(Submit answers by 01/23/2023)
A 245 g mass is on a string and is traveling clockwise in a vertical circle with a radius of 65.0 cm. Because of gravity, the mass goes a bit slower at the top, and a bit faster at the bottom. When it is at its lowest point, it is 55.0 cm from the floor, and there is a tension of 14.5 N in the string. Treat the mass as a particle, and neglect friction. Use g = 9.81 N/kg
When it reaches the very top of its trajectory, the string magically disappears. What horizontal distance to the right of the center of the circle does the mass travel before striking the ground?
We have five solutions to this. No, wait, just one - Ben Nickle!!!!
W00000000OOOOOOOO000000000T!!!!
Problem 4: Projectile Block on an Incline
(Submit answers by 01/16/2022)
A small block starts at rest 1.85 m from the bottom of a 25.0o incline. It accelerates down the incline, and leaves the end 1.12 m above the floor.
What horizontal distance does it travel before striking the floor if the coefficient of friction between the block and the incline is 0.114? Treat the block as a particle for the purposes of this question. (i.e. don’t worry about the size of the block or its dimensions)
We have a grrrrrrreat solution by Ben Nickle!!
Problem 3: Two Blocks on an Incline
(Submit answers by 12/16/2022)
Two blocks are connected by a string as they slide down an incline that makes a 34.0o angle with the horizontal. The 13.0 kg block has a coefficient of friction of 0.618, and an 8.50 kg block has a coefficient of friction of 0.117 with the plane. Calculate the tension in the string.
(Adapted from Douglas C. Giancoli's Physics)
We have a great solution by Ben Nickle!!
(Submit answers by 12/5/2022)
A 235 gram sphere (sphere A) is at rest with a charge of +11.5 micro Coulombs. Another sphere (Sphere B) has a charge of +31.5 micro Coulombs and a mass of 385 grams and is at rest a distance of 1.00 m from the first sphere. Neglect any form of friction , or gravity.
If they are released simultaneously, what are their velocities when they are very far apart? What are their velocities when they are only 2.00 m apart?
Sphere B is released first. When it is exactly 2.00 meters from sphere A, sphere A is released. What are their velocities then they are very far apart?
Suppose only sphere B is released, and sphere A is held stationary. What is the velocity and position of sphere B after 0.500 seconds?
So far we have just Ben Nickle and Chris Murray for this one. Ben's solution uses Desmos and phase space to solve the simultaneous energy and momentum equations. I just bludgeon the problem with algebra, but at some point, I use the solver to get my answer to #2. Neither one of us knows how to solve #3, so Ben wrote a program, and I used Interactive Physics.
(Submit answers by 11/28/2022)
Two trains going different speeds are accidentally on the same track. The express train going 35.0 m/s initially discovers the error when it is 80.0 meters behind the local commuter train that is going 20.0 m/s in the same direction. The engineer on the express train hits the brakes to find that the rate of deceleration is only 1.2 m/s/s. Assume that the speed of the commuter train is constant.
A. Do the two trains hit? (or do they avoid collision?) If they do collide, B. how far does the express train travel before striking the commuter train, and what is the C. relative speed of the two trains when the collision occurs? (i.e. the speed of the collision)
Suppose the commuter train engineer started to accelerate at the same instant the express train engineer started to decelerate, D. what minimum rate of acceleration on the part of the commuter train would avoid a collision?
I received three very good solutions for this - Caleb Singh submitted the first solution (hours after I put this up) and it is a very complete and nuanced solution with algebraic steps. Ben Wyland submitted a very succinct answer with a unique way to calculate whether the collision occurred, and Ben Nickle submitted a very elegant solution with Desmos graphs and calculus.