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PHY131H1S – Class 19

Today: •  Review for test

tomorrow on Chs.6-12 •  Solving Equilibrium and

Non-Equilibrium problems

•  Impulse and Momentum

•  Work and Kinetic Energy

Test Tomorrow •  6:00pm to 7:30pm. Students will be admitted into

the room at 6:00, test will actually begin at 6:10. •  Students whose last names begin with A to LIU will

write in GB404 •  Students whose last names begin with LU to Z will

write in GB412 •  Allowed aids include a non-communicating

calculator and a single aid-sheet prepared by the student, no larger than 8.5”x11”, written on both sides.

•  Test covers Chapters 6 through 11 plus sections 12.1 through 12.4, and 12.9

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Recall from last time: Four Ts are made from two identical rods of mass, m, and length L. Find the moments of inertia about the dotted line.

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The Parallel-Axis Theorem •  Suppose you know the

moment of inertia of an object when it rotates about axis 1: I1

•  You can find the moment of inertia when it is rotating about an axis 2, (I2) which is a distance d away:

I2 = I1 + Md 2

Four Ts are made from two identical rods of mass, m, and length L. Find the moments of inertia about the dotted line.

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Basic Idea of Dynamics:

In-Class Discussion Question 1. A Martian lander is approaching the surface. It is slowing its descent by firing its rocket motor. Which is the correct free-body diagram for the lander?

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In-Class Discussion Question 2. The terminal speed of a Styrofoam ball is 15 m/s. Suppose a Styrofoam ball is shot straight down with an initial speed of 30 m/s. Which velocity graph is correct?

Strategy for Solving Dynamics Problems

•  Draw a sketch of the situation and write down knowns and unknowns

•  Draw a free-body diagram •  Choose x,y axes, note if there is acceleration •  Find x,y components of all forces and sum to

find (Fnet)x and (Fnet)y

•  Equilibrium: set (Fnet)x=0 or (Fnet)y=0

•  Non-equilibrium: set (Fnet) = max or (Fnet)y = may

•  Solve for the unknown you want

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Rolling Without Slipping For an object that is rolling without slipping, there is a rolling constraint that links translation and rotation:

In-Class Discussion Question 3. The propulsion force on a car is due to

A.  tension B.  static friction. C.  kinetic friction. D.  thrust from the car engine. E.  the applied force.

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In-Class Discussion Question 4. Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1?

A.  greater than rope 2 B.  less than rope 2 C.  equal to rope 2

In-Class Discussion Question 5. A ball on a string is swung in a vertical circle. The string happens to break when it is parallel to the ground and the ball is moving up. Which trajectory does the ball follow?

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Momentum is the product of a particle’s mass and velocity, has units of kg m/s, and is given by

The impulse upon a particle is defined as

Impulse has units of N s, but you should be able to show that N s are equivalent to kg m/s. The impulse-momentum theorem is

A.  vf = v2. B.  vf is less than v2. C.  vf is greater than v2, but less than v1. D.  vf = v1. E.  vf is greater than v1.

In Class Discussion Question 6. The two particles are both moving to the right. Particle 1 catches up with particle 2 and collides with it. The particles stick together and continue on with velocity vf. Which of these statements is true?

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What is “Work”?

In Class Discussion Question 7. A box slides along the frictionless surface shown in the figure. It is released from rest at the position shown. Is the highest point the box reaches on the other side at level a, at level b, or level c?

A.  At level a B.  At level b C.  At level c

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In-Class Discussion Question 8. A fireman slides down a pole at constant speed. This is a situation in which A.  U → Eth. Emech is

conserved. B.  U → Eth. Emech is not

conserved but Esys is. C.  U → Wext. Neither Emech

nor Esys is conserved. D.  U → K. Emech is not

conserved but Esys is. E.  K → Eth. Emech is not

conserved but Esys is.