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# Dynamics: Cause of Motion - PowerPoint PPT Presentation

Dynamics: Cause of Motion. Sections 7.1 , 7.2. Updates/Reminders. Test #2 has been moved from Tuesday next week to Thursday next week due to a need for more time to prepare for content. Addresses Chapters 4, 6, and 7. Next reading quiz due prior to class on Tuesday

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Dynamics: Cause of Motion

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## Dynamics: Cause of Motion

Sections 7.1 , 7.2

• Test #2 has been moved from Tuesday next week to Thursday next week due to a need for more time to prepare for content.

• Addresses Chapters 4, 6, and 7.

• Next reading quiz due prior to class on Tuesday

• LAB A4-PM: Projectile Motion due Friday 4pm

• Weekly Reflection #7 sent out on Friday morning

• Final Exam Thursday, Dec 11, 10am-12:00pm

### Conservation of Momentum

• Demonstration: the total momentum of an isolated system is conserved. That is, pi = pfif and only if we have an “isolated system” – no unbalanced outside forces.

• Example 1 – the collision of carts

• Example 2 – the “explosion” of carts

• Example 3 – the addition of mass

### Numerical Problem 1

• A truck with a mass of 3,000kg and a velocity of +20m/s collides head on with a car of 1,500kg mass and a velocity of -20m/s. If the vehicles stick together, what is the resulting motion of the pair?

• Solve using conservation of momentum; that is, pi = pf.

### Numerical Problem 2

• Two dynamics carts are separated by a compressed spring. The mass of cart 1 is twice the mass of cart 2; that is, m1=2m2. The spring is released and the carts fly apart. If cart 1 has a velocity of +3m/s, what is the velocity of cart 2?

### Numerical Problem 3

• A train car (mass 11,200kg) is moving along at a speed of +2m/s. A 5,000kg mass of coal with no horizontal motion is dropped into the hopper of the train car. What is the resulting motion of the train car now loaded with coal?

### The Second Law of Motion

• a.k.a. Newton’s Second Law

• The net instantaneous force acting on an object is precisely the instantaneous change of its momentum per unit time. In symbols, the second law can be written as F = Δp/Δt with Δt very small.

• Note that F and Δp are vectors.

• Not very enlightening; time for an experiment.

### Newton’s Second Law

• Experiment:

• Acceleration as a function of force (constant mass system)

• Acceleration as a function of mass (constant force system)

• Results:

• a is proportional to F

• a is inversely proportional to m

• Conclusion: F = kma; k=1 if F defined to be in Newtons, N

### Second Law Reprise

• F = Δp/Δt

• F = Δmv/Δt

• F = mΔv/Δt

• F = ma

• Both F and a are vectors; m is a scalar.

• The sum of forces acting on a body produce an acceleration inversely proportional to mass.

• ΣF=ma (where F is expressed in Newtons)

### 2nd Law Problem – Examples

• What is the weight of a person with a mass of 81kg. Note that g = 9.8m/s2.

• An car with a mass of 1,500kg accelerates at a rate of -2m/s2 under a constant force. What are the magnitude and direction of that force?

• How much force would it take to slow a 75kg person riding in a car going +20m/s to a complete stop if the time was 0.03 seconds – the typical time of an auto collision?

### More Examples of Newton’s 2nd Law

• An object accelerates at a rate of 1.5m/s2 under a force of 53N. What is its mass?

• How much upward force does the ground apply to someone with a mass of 75kg to counter balance the pull of gravity? Note that g = -9.8m/s2 and that Fnet = ma and that a = g.

• A force of 7.0N is applied to a 3.5-kg mass for 2.0 seconds. What is the change of velocity?