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Key Steps to Solving Dynamics Problems:
Define the system and coordinate system.
Create Free-Body Diagrams indicating forces
ΣF=ma The sum of the forces acting on the system determine the acceleration of the system.
USE LOTS OF PAPER!!!
There are four main types of problems associated with Unbalanced Forces Calculations, samples of each type of problem are below:
Modified Atwood
Elevator Ride
Rocket Launch
Motion on a Ramp
1a. Modified Atwood - A
1a. Modified Atwood - A
Which system has the greatest net force? Explain how you know.
Which system has the least inertia? Explain how you know.
Determine the acceleration for each system in terms of M and g.
1b. Modified Atwood - B
1b. Modified Atwood - B
In a contrived lab setup, a 5-kg cart (m_1) is placed on a frictionless surface. It is pulled by a massless string over a frictionless, massless pulley which is attached to a 2-kg hanging mass (m_2). You may be asked to determine the following:
Determine the acceleration of the 5-kg cart.
Determine the Force Tension in the string while the system is accelerating.
Suppose the surface wasn't frictionless and the µ_k = 0.2. Determine the new acceleration of the cart.
Atwood.pdf2. Elevator Ride
2. Elevator Ride
Suppose that you entered the elevator carrying a package. Would the package feel heavier or lighter during certain parts of the ride? Defend your answer!
Questions to Consider:
Questions to Consider:
Have you ever felt heavier or lighter when riding in an elevator? Is this sensation caused by the music or by the motion of the elevator? Does everyone feel heavier or lighter at the same times?
Describe the times in the elevator when you feel your “normal” weight.
Describe the times in the elevator when you feel heavier than your “normal” weight.
Describe the times in the elevator when you feel lighter than your “normal” weight.
Do these “feelings” occur when you are moving at a constant speed or when you are accelerating?
You discover in the last activities that unbalanced forces always produce accelerations.
What seems to be the relation between the direction of the FNet and the acceleration?
Quick Experimentation:
Quick Experimentation:
Hang a 0.50 kg or 1.0 kg mass on the end of a spring balance and record the force reading on the balance.
Fg = ___ N
Start the mass just above the floor and try to lift the mass to simulate an elevator ride.
Describe the force reading when the mass was accelerating upward, then moving at a steady speed, then slowing down (accelerating downward).
Next, start the mass at about 2.0 meters above the floor and perform the downward ride, stopping before the kg hits the floor.
Describe the force reading when the kg was accelerating downward, then moving at a steady speed, then slowing down (accelerating upward).
Problem Solving:
Problem Solving:
An elevator ride to the top of a tall building has three phases:
beginning the ascent by accelerating upwards,
traveling at a constant velocity, and
slowing to a stop by accelerating downwards.
Analyze the data above, from a trip from the ground floor of the Grade 4-5 Building at ACS to the 3rd floor and the returned to the ground floor of a 7.2 kg mass.
At the beginning of the trip, the elevator accelerates (ay) upward at 1.5 m/s2.
Construct a force diagram for the passenger.
Express the force the floor exerts on the passenger (FN) in terms of ay, m and g.
Relate your equation you derived to the graph above, which portion of the graph does your equation describe?
Calculate the force the floor exerts on the passenger.
Explain how the tension in the cable supporting the elevator relates to the force normal acting on the passenger.
The elevator is moving up at a constant velocity of 3.5 m/s, as illustrated in the diagram below: The passenger has a mass of 7.2 kg.
Construct a force diagram for the passenger.
Express the force the floor exerts on the passenger (FN) in terms of m and g.
Upon reaching the top of the building, the elevator accelerates downward at 2.5 m/s2.
Construct a force diagram for the passenger.
Express the force the floor exerts on the passenger (FN) in terms of ay, m and g.
Calculate the force the floor exerts on the passenger.
While descending in the elevator, the cable suddenly breaks. Express the force the floor exerts on the passenger (FN) in terms of ay, m and g. Explain your answer.
Elevator Prob.pdfPlease download and open the following file with Vernier Graphical Analysis:
Gr45 Elevator ACS.gambl
On its first flight the SpaceX Falcon Heavy carried a Tesla Roadster into space.
The Falcon Heavy has a mass of 1.42x10^6 kg at launch. The 27 Merlin engines each produce 845 kN of thrust.
Rocket Prob.pdfConstruct a free-body diagram of the Falcon9 at t = 5 s.
According to the given data (mass and thrust) and your free-body diagram, determine the expected acceleration at t = 5s.
How does this compare with the data given in the graph?
In the graph above, there are two distinct trend lines (blue = 0-15 s) and (red = 20-35s). Comment on the difference in acceleration between the two time period.
4. Pulled up a Ramp / Coasting Down a Ramp
4. Pulled up a Ramp / Coasting Down a Ramp
A child takes a trip down a slide.
Draw a quantitative force diagram for the 30kg child. The frictional force is 160 N.
Determine the coefficient of kinetic friction.
Write an equation for the forces on the child parallel to the slide and find the net force on the child.
Calculate child's acceleration.
As the child approaches the bottom of the ramp, the angle of the slide decreases. Describe the effects on the child’s velocity and acceleration.
Practice Problems
Practice Problems
AP Unbalanced Forces Problems
AP Unbalanced Forces Problems
Net Force Problem Solving
Topic 2 Problems (12-23) - In the folder to the right (2016_Topic_2_Answers_2.2.pdf)
Pumpkin Bungee Problem
Pumpkin Bungee Problem
Given a pumpkin from the choices below, make note of its mass directly underneath the pumpkin. Use the scale on the left to determine the height of the pumpkin, not its stem.
Developing Proficiency (2) - Able to identify the various types of energy and forces present at various points within the scenario.
Demonstrating Proficiency (3) - Able to determine, quantitatively, the values for the questions below.
Extending Proficiency (4) - Able to create a generalized model that will identify the essential variables and create mathematical functions that will allow a user to answer the questions below in as few calculations as possible (think spreadsheet).
Given the spring that you were assigned, attach to your pumpkin securely where the pumpkin meets its stem. The other end of the spring would attach to the top of our classroom, 2.6 m above the ground. You will be dropping the pumpkin after you hold it up against the ceiling with the spring slack. Assume the spring cannot be overstretched or deformed.
For clarity, Diego stated the system he was working with was the Pumpkin (mass), Earth, and spring. Therefore, he derived the following equation to describe the energies in the system: Eq 1:
Additionally, he chose his starting point (near the ceiling) as ∆y = 0m.
Ultimately arriving at the equation for the total distance the mass will fall (∆y) to be: Eq 2
Using the diagram above, clearly label the following values: ∆y, m, L, x, h and k.
Using the LCE, show how Diego derived Eq 2.
On the diagram above,
Regions: In the regions indicated by A, B and C, describe the changes to the motion of the pumpkin within each of these regions.
Include; changes to FBDs, Energy Pie Charts, and Motion Maps.
Points: At each of the points, indicate the specific forces (FBDs) and forms of energy (EPCs) acting at that point.
Diego has determined that at point 3 in the diagram above the forces acting on the pumpkin are in equilibrium. Express the extension of the spring (x) in terms of m, g, and k as appropriate.
**By using the conservation of energy, Diego then determined that the pumpkin was traveling at the greatest velocity a position #3. Express the velocity (vmax) of the pumpkin in terms g, L, m and k, as appropriate.
Express the maximum extension (x) of your chosen spring in terms of m, g, k, L and h, as appropriate.
Show your work to determine if your pumpkin survives the bungee jump. Survival would mean it does not touch the ground when dropped from the height of the ceiling from your spring. Include diagrams, equations and calculations.
If your pumpkin survives the bungee jump, determine the maximum velocity it experiences during the drop.
If your pumpkin does not survive the bungee jump, determine the speed at which it hits the ground.
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