Collection of Physics Problems

Announcement

noreply@blogger.com (Unknown) — Sat, 14 Mar 2009 23:58:00 +0000

I can't provide some new problems from now (~~maybe until the end of April~~) because I'm busy preparing myself for National Exam. (and also other business)
Therefore, if you want to become a contributor of this blog by providing some physics problems with solutions, you can leave comment below.
Thank you for your sincerity.

Leak Charge

noreply@blogger.com (Unknown) — Fri, 13 Mar 2009 13:39:00 +0000

A conductor ball of radius R is charged with charge Q0. The ball is placed in an infinite space filled with a material with conductivity σ and permittivity ε, so the charge leaks away from the ball.
Find the remaining charge on the ball as function of time!

Click here to read the solution.

Semi-infinite RLC Circuit

noreply@blogger.com (Unknown) — Wed, 11 Mar 2009 13:58:00 +0000

Consider a semi infinite circuit like shown above. Magnitude of impedance of inductor and capacitor equal to R (i.e. ωL=1/ωC=R). Find the total impedance of the circuit!

Click here to read the solution.

Turning Scooter

noreply@blogger.com (Unknown) — Mon, 09 Mar 2009 13:49:00 +0000

A scooter of length l has two wheels. The scooter moves with CM's speed v on a rough plane and is going to turn its direction without change its speed. To turn its direction, the front wheels is rotated to an angle θ.
Calculate the minimum coefficient of friction between the plane and the wheels, μ, so that the scooter does not slip to the plane! Assume CM of the scooter is at the middle.

Click here to read the solution.

Winding Spring

noreply@blogger.com (Unknown) — Sat, 07 Mar 2009 13:37:00 +0000

A uniform solid cylinder of mass M and radius R can freely rotate around its axis O. And there is a spring of relaxed length L and stiffness K attached to the cylinder and a static wall. See picture below.Initially, the spring is relaxed. As the cylinder starts rotating, the spring will wind the cylinder. The surface of cylinder is very rough, so that the spring does not slip with the cylinder's surface.
Find the minimum initial angular speed of the cylinder, ω0, so that it can rotate to angle 2π!

Click here to read the solution.

Minimum Friction

noreply@blogger.com (Unknown) — Thu, 05 Mar 2009 13:17:00 +0000

A uniform rod of mass M and length l is placed on a rough floor and a rough wall. The rod makes an angle θ to the floor.What is the minimum coefficient of friction of the floor and the wall in order to prevent the rod from slipping? Assume the floor and the wall made by the same material.

Click here to read the solution.

Breaking A Ruler

noreply@blogger.com (Unknown) — Tue, 03 Mar 2009 14:46:00 +0000

Why is it much easier to break a ruler by bending it than by pulling it?

Click here to read the solution.

Trapping Lenses

noreply@blogger.com (Unknown) — Sun, 01 Mar 2009 08:32:00 +0000

Some identical thin convex lenses are arranged at edge of a full circle of radius R, according to the picture below. The lenses have equal angle spacing of θ (θ<<1). Each lens has aperture length of D (D<<R).Find the longest focus distance, f, of the lenses so that it is possible to trap a ray of light inside the circle!

Click here to read the solution.

Spring and Hanging Ball

noreply@blogger.com (Unknown) — Fri, 27 Feb 2009 13:53:00 +0000

A small ball of mass M is hung with a spring of stiffness k and zero relaxed length. The ball is in gravitational field, g. Then the ball is brought down to a point (x0, y0) as shown in picture below, and then released.How will path of the ball? And also find coordinate of the ball when it reaches its highest position!

Click here to read the solution.

Rotating Sprayer

noreply@blogger.com (Unknown) — Wed, 25 Feb 2009 14:02:00 +0000

A sprayer consists of four bent pipes of length 2a for each pipe. The pipes can freely rotate about point O without friction.An ideal fluid of mass density ρ flows into the sprayer through point O from a large tank of pressure P (assume it's much larger than atmospheric pressure).
After a long time, the sprayer reaches a constant angular velocity, ω. Ignore gravity, energy lost, and turbulence of fluid.
Calculate ω!

Click here to read the solution.

V Track

noreply@blogger.com (Unknown) — Mon, 23 Feb 2009 14:02:00 +0000

A track consists of two rough planes forming an angle 2θ to each other. It's symmetric to vertical axis and makes an angle φ to the horizontal.
Coefficient of friction of the planes are different. The left side is μ0 and the right side is μ.
Then a ball of radius R and mass M (moment inertia I=ηMR^2) is placed on the track.

As the ball moves, it slips with left side of the track and does not slip with right side of the track.
Find the minimum value of μ! (in μ0, φ, and θ)

Click here to read the solution.

Complex Circuit

noreply@blogger.com (Unknown) — Sat, 21 Feb 2009 13:46:00 +0000

A complex circuit consists of some resistors. An ideal current source is then connected through two points at the circuit. Then an ideal voltmeter is connected to two nodes of a resistor in the circuit. Reading of the voltmeter is V.Then the voltmeter is substituted with an ideal ammeter. The reading is I.
If the current source is then disconnected to the circuit and the ammeter is substituted with ohmmeter, prove that reading of the ohmmeter is V/I!

Click here to read the solution.

Semicircle Charged Arc

noreply@blogger.com (Unknown) — Thu, 19 Feb 2009 12:38:00 +0000

A semicircle arc is charged with charge density distribution at a point, , where λ is total charge in a unit length and α is angle between the diameter and its position.Calculate the ratio of electrical potential at point A and point O!

Click here to read the solution.

V-shaped Rod Path

noreply@blogger.com (Unknown) — Tue, 17 Feb 2009 13:20:00 +0000

Consider two rods forming V-shape with angle θ and a ball, of radius r, mass m, and moment inertia I, on it. See picture below.
The ball is released at position l from rods' adjacent and start moving because of gravitational acceleration, g. The rods are rough enough, so it prevents the ball from slipping in its movement.
Calculate the initial angular acceleration of the ball!

Click here to read the solution.

Multiple Collisions (2)

noreply@blogger.com (Unknown) — Sun, 15 Feb 2009 13:00:00 +0000

Consider the same case from previous problem. But there is an external force works on the block, and bring the block up to a height of 2h very slowly.
Find the final average velocity of the ball!

Click here to read the solution.

Multiple Collisions

noreply@blogger.com (Unknown) — Fri, 13 Feb 2009 12:47:00 +0000

In picture above, a small ball of mass m moves with average velocity v vertically up and down due to collisions with a block of mass M and a floor. The block is floating in the air due to the collisions with the ball.
Find h, the average height of the block!
Gravitational acceleration g. Assume and .

Click here to read the solution.

Two Batteries Circuit

noreply@blogger.com (Unknown) — Wed, 11 Feb 2009 06:59:00 +0000

By what percentage would the current I increase if switch S is closed?

Click here to read the solution.

Maximizing Amplitude

noreply@blogger.com (Unknown) — Mon, 09 Feb 2009 14:51:00 +0000

A block of mass m is oscillating with a spring of stiffness k. See the picture.In order to increase its amplitude, one of end of the spring (point A) is suddenly moved with a velocity v to the left and kept moving with that velocity.
Determine when it should be suddenly moved in order to maximize its amplitude!
How's the result if it's not suddenly moved, but accelerated by a to the left!

Click here to read the solution.

Two Swinging Ball

noreply@blogger.com (Unknown) — Sat, 07 Feb 2009 01:42:00 +0000

Two small balls of mass m are hung by strings of length l to a static nail. The balls are connected with a massless rod of same length, l. Initially, the balls are held at position like shown below.The balls are then released and start moving down.Calculate the maximum tension, T, of a string during the motion!

Click here to read the solution.

Modified Series Capacitors

noreply@blogger.com (Unknown) — Thu, 05 Feb 2009 05:37:00 +0000

Consider 2 capacitors with same areas in series as shown in the picture. One of them is placed between the another one's plates. The wider capacitor have capacitance C and have distance twice of the narrower one.
Calculate the net capacitance of the circuit!

Click here to read the solution.

Rolling Pencil

noreply@blogger.com (Unknown) — Tue, 03 Feb 2009 13:30:00 +0000

A pencil can be modeled as a hexagonal prism (in this case). When a pencil rolls on a rough floor, it will rotate around one of its edge, and then the next edge will hit the floor, and then the pencil will continue rotating with the edge as a new rotation axis. To simplify the problem, assume mass of the pencil is concentrated at its center.Calculate the minimum value of coefficient of friction between the pencil and the floor so that the pencil doesn't slip when its edge hits the floor!
Assume the contact between the pencil and floor only occurs at the pencil's edge.

Click here to read the solution.

Hanging Rod

noreply@blogger.com (Unknown) — Sun, 01 Feb 2009 08:07:00 +0000

A uniform rod of length l and mass m is hung by two strings of length l at its two ends, like picture below. Then the rod is rotated to an angle θ and released without any initial velocity or angular velocity.
Calculate the magnitude of acceleration, a, experienced at its end (point A) immediately after it's released!
Click here to read the solution.

Rotating Square

noreply@blogger.com (Unknown) — Fri, 30 Jan 2009 14:43:00 +0000

A uniform flat square is placed on a rough floor. If the square is rotated around its edge, it takes time t to completely stop.
Calculate the time it takes ,t', to completely stop if it's rotated around its center with same initial angular velocity!
Click here to read the solution.

Swinging Ball on Rough Inclined Plane

noreply@blogger.com (Unknown) — Thu, 29 Jan 2009 14:17:00 +0000

A ball of mass m is hang by a string of length l on a rough inclined plane with coefficient of friction μ and angle θ with the horizontal (μ=tanθ). Initially the ball is at the lowest position.
Calculate the minimum initial velocity, v, should be given to the ball to make a full circle of its path!

Click here to read the solution.

Capacitors Circuit

noreply@blogger.com (Unknown) — Tue, 27 Jan 2009 14:28:00 +0000

Five capacitors are arranged in a circuit like shown above. Two of them have capacitance of C and are initially charged with charge Q on each capacitor. While the other have capacitance of 2C and are not charged.
Find the final charge Q' on the middle capacitor!