4ASolutions

Physics 4A

Course Syllabus

Two past exams (including two finals) with no solutions and a couple of first and second exams with their solutions:

First Exam Solutions Archives.
Second Exam Solutions Archives.

4A Lab Exercise Manual (not fully developed yet and never will be.)

One dimensional kinematics:

Other problems of interest with solutions:

Find the distance a falling ball travels with respect to the earth when it falls from the ceiling to the floor of an accelerating elevator.

Finding the ratio of two heights for two vertically colliding balls.

Flower pot falling past a window

The time it takes for two missles to collide

The distance at which a speeding car (with zero acceleration) and a cop car (zero initial velocity and acceleration, a) meet again.

The total time it takes a police car to catch a speeding car after the police car has accelerated to a maximum velocity.

Finding the distance (relative to the ground) a ball travels when released from the ceiling of an elevator (of height H) which moves at constant velocity upward. This is a rather "plodding" solution of mine, not very elegant, but it gets the job done.

Finding the time of flight of a ball dropped from an elevator moving upward at constant velocity as viewed from the ground.

Two dimensional kinematics:

Homework Set 2

Other Problems of interest with solutions:

Finding the total horiztontal distance travelled from the origin by the second of two pieces after a horizontal explosion at the top of a projectile's flight. The solution is not entirely proved in detail but is acceptable.

Finding the final speed of a horizontally projected object knowing its initial launch height and range.

Finding the "point of aim", D, veritcally above a target on level ground with the launched projectile in terms of the range and initial speed.

Finding the initial firing angle of a ball with respect to the ground tossed vertically upward from a horizontally moving train.

Showing that the final speed of a projectile is independent of its initial firing angle

Finding the maximum range of a projectile

Seven pages of kinematics examples with vectors
page 1: page 2: page 3: page 4: page 5: page 6: page 7

An example of relative velocity in navigation:
A ferry boat crossing a river (Page One)
A ferry boat crossing a river (Page Two_

Newton's laws (no friction and no circular motion)

Homework Set 3

Finding the two different accelerations involving sliding friction between two bodies.

Accelerometer (Finding the acceleration of a mass by the angle its supporting string makes with the veritcal.)

Finding the force between two blocks when one of them is pushed by an applied force

Finding the acceleration (relative to the earth) of the two masses in an Atwood's machine when the machine is in an accelerating elevator, as worked from the non-inertial frame of the elevator and then transferred with an acceleration "mnemonic" into the earth's frame. Solution by Jamie Mcguire, De Anza physics major.

Finding the acceleration (relative to the ground) of the heavier of two masses in an Atwood's machine when the machine is in an accelerating elevator as worked from the inertial frame of the earth.

The accelerating elevator problem, but finding the tension force.

more on Newton's laws with friction and/or circular motion

Exam 1 after this chapter

Work and Kinetic Energy

How much work to raise a rope from a table at constant kinetic energy.
Actually, the question SHOULD ask how much work to raise the rope at constant velocity!!
At constant kinetic energy, its a different problem. Do you see why?

The general work-energy theorem

Homework Set 6

Find the potential energy function for a mass attached to pendulum and a spring as a function of the displacement angle.

Finding the final speed of a mass released from rest while attached to a pendulum and a spring.

Finding the tension from a string of length l on a mass at the top of its swing after it has swung down from a horizontal position,
and hit a fixed peg a distaince D below the top of the swing. (See the diagram on the solution)

Finding the maximum distance a mass slides up an inclined plane after being launched by a spring

The tension on a mass at the bottom of its swing from a horizontal position initially at rest.

Finding the maximum compression of a spring when a weight is dropped onto it

Finding the maxiumum kinetic energy of a falling body as it compresses a spring.

Center of mass and momentum conservation

Finding the average force on a digital balance from a stream of small masses boucing onto and away from it.

Finding the maximum compression of a spring between two masses that are each moving while they collide.

Finding the horizontal speeds of a mass and the wedge the mass it just slid down on.

The force as a function of time on a pan balance as a rope is allowed to fall onto it.

How far a cart moves when a mass on the cart moves from one side to the other

Rotational kinematics and dynamics

Finding the speed of the tip of a rod hanging initial at rest from a pivot on the other end after being struck by an impulsive force.

Finding the speed of a point mass attached to a disk after it has rotated with the disk from the top to the bottom of its path.

Finding the tension force on a hanging mass from a string wound around a rotating sphere.

Exam 2 should be here

Universal Law of Gravitation

Homework Set 9

Finding the tension force between two equal masses (tied together with a stretchless rope of length l) as they together freely accelerate toward a planet (i.e., finding the tidal force on a body).

Finding the distance of closest approach of a body with a non-zero initial velocity infintely far away from a fixed planet.

Finding the velocity of one of two masses approaching each other under mutual gravitational attraction (find the mistake?).

Finding the force from a sphere on a rod

Finding the relation between the orbit speed and the escape velocity of a body

Homework Set 10
Oscillations