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Physics 114A - Mechanics Lecture 4 (Walker: 2.6-7) Equations of Motion January 10, 2014

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### Physics 114A - MechanicsLecture 4 (Walker: 2.6-7)Equations of MotionJanuary 10, 2014

### End of Lecture 4

John G. Cramer

Professor Emeritus, Department of Physics

B451 PAB

Announcements

- Homework Assignments #1-3 are now available on WebAssign. Assignment #1 is due at 11:59 PM on Thursday, January 16. Be sure to do the “A” homework (not “B”). So far 167/218 students have registered for 114A on WebAssign. Everyone MUST register on WebAssign before Exam 1.
- Obtain a H-iTT clicker from the University Bookstore. RF Clickers should be set to Channel 01. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page. So far 110/218 students have registered their clickers.
- If you are disabled and plan to take the 114A exams at the DRS Office in Mary Gates Hall, see me as soon as possible to make arrangements.
- The 117 labs start on Monday. By 8:00 AM on the day of your lab, you must have completed the Pre-Lab exam on WebAssign.

Physics 114A - Lecture 4

Motion with Constant Acceleration

Physics 114A - Lecture 4

Motion with Constant Acceleration

Velocity: (2-7)

Average velocity: (2-9)

Position as a function of time:

(2-10)

(2-11)

Velocity as a function of position:

(2-12)

Physics 114A - Lecture 4

Motion with Constant Acceleration, Other Variables (1)

Physics 114A - Lecture 4

Motion with Constant Acceleration, Other Variables (2)

Physics 114A - Lecture 4

Motion with Constant Acceleration

The relationship between position and time follows a characteristic curve.

Parabola

Physics 114A - Lecture 4

- Assume that the brakes on your car create a constant deceleration, independent of how fast you are going. Starting at a particular speed, you apply the brakes and note the stopping distance D and the stopping time T.
- Now you double the speed of the car. How does this change affect the stopping distance Dand the stopping timeT?
- D and T remain the same.
- D and T both double (i.e., x2).
- D doubles and T quadruples (i.e., x4).
- D quadruples and T doubles.
- D and T both quadruple.

Physics 114A - Lecture 4

An object falling in air is subject to air resistance (and therefore is not freely falling).

Physics 114A - Lecture 4

Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.

+

We will normally use the valueg = 9.81 m/s2.

Physics 114A - Lecture 4

Free Fall and g

One important example of constant acceleration is the “free fall” of an object under the influence of the Earth’s gravity. The picture shows an apple and a feather falling in vacuum with identical motions.

The magnitude of this acceleration, designated as g, has the approximate value of a = g = 9.81 m/s2 = 32.2 ft/s2.

If downward is designated as the +y direction, then a = +g; if downward is designated as the -y direction, then a = -g.

(Note that g is always positive., but a may have either sign.)

Physics 114A - Lecture 4

Velocity

Acceleration

Freely Falling Objects

Trajectory of a projectile:

Physics 114A - Lecture 4

Problem Solving Strategy for 1-D Motion with Constant Acceleration

Picture - Determine if the problem is asking you to find time, distance, velocity, or acceleration for an object.

Solve - Use the following steps to solve problems that involve one-dimensional motion and constant acceleration:

- Draw a figure showing the particle in its initial and final positions. Include a coordinate axis and label initial and final coordinates of the position.
- Select one or more of the constant-acceleration kinematic equations. Solve them algebraically for the desired quantities. Then substitute in the given values and evaluate the answer.
- Repeat as needed.

Check - Make sure your answers are dimensionally consistent. Make sure the magnitudes of your answers are in the expected “ballpark”.

Physics 114A - Lecture 4

Example: The Flying Cap

Upon graduation, a joyful student throws her cap straight up in the air with an initial speed of 14.7 m/s. Given that its acceleration has a magnitude of 9.81 m/s2 and is directed downward (we neglect air resistance),(a) When does the cap to reach its highest point?(b) What is the distance to the highest point?(c) Assuming the cap is caught at the same height it was released, what is the total time that the cap is in flight?

- Draw the cap (as a dot) in its various positions.
- (a) Use the time, velocity and acceleration relation.(b) Use average velocity: vav = v0/2 = 7.35 m/s;Dx = vavDt =(7.35 m/s)(1.5 s) = 11.0 m(c) Up time = down time, so total time is 3.0 s. (see text for a more complicated method.)

3. The answers have the right units and seem reasonable.

Physics 114A - Lecture 4

Example: The Flying Cap (continued)

The height of the cap vs. time has the form of a parabola (since x ~ t2). It is symmetric about the midpoint (but would not be, if air resistance were present).

The velocity of the cap vs. time has the form of a straight line (since v ~ t). The velocity crosses zero at the midpoint and is negative thereafter, because the cap is moving downward.

Physics 114A - Lecture 4

Example: A Traveling Electron

An electron in a cathode-ray tube accelerates from rest with a constant acceleration of 5.33 x 1012 m/s2 for 0.150 ms, then drifts with a constant velocity for 0.200 ms, then slows to a stop with a negative acceleration of-2.67 x 1013 m/s2. (Note: 1 ms = 10-6 s)

How far does the electron travel?

- Draw the electron (as a dot)in its various positions xi.
- Calculate the displacement Dxi and velocity vi for each part of the path:

3. The answers have the correct units and appear to be reasonable.

Physics 114A - Lecture 4

Example: Speed of a Lava Bomb

A volcano shoots out blobs of molten lava (lava bombs) from its summit. A geologist observing the eruption uses a stopwatch to time the flight of a particular lava bomb that is projected straight upward.

If the time for it to rise and fall back to its launch height is 4.75 s, what is its initial speed and how high did it go? (Use g = 9.81 m/s2.)

Physics 114A - Lecture 4

Before the next lecture on Monday, read Walker, Chapter 3.1-3.3

- The 117 labs start on Monday. By 8:00 AM on the day of your lab, you must have completed the Pre-Lab exam on WebAssign.
- Homework Assignments #1-3 are now available on WebAssign. Assignment #1 is due at 11:59 PM on Thursday, January 16. Be sure to do the “A” homework (not “B”). So far 167/218 students have registered for 114A on WebAssign. Everyone MUST register on WebAssign before Exam 1.
- Obtain a H-iTT clicker from the University Bookstore. RF Clickers should be set to Channel 01. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page. So far 110/218 students have registered their clickers.
- If you are disabled and plan to take the 114A exams at the DRS Office in Mary Gates Hall, see me or Susan Miller as soon as possible to make arrangements.

Physics 114A - Lecture 4

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