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Original question from the book: Logs dropped upright into a pond do not remain upright, but float ‘flat’ in the water. Explain. A long log can float vertically but this position of equilibrium is unstable. So, a slight tilt will make it tilt further from the vertical position until it reaches...

:ok::thumbup:

Thank you very much for the explanation.

Given that 0 < sin x < x is true for 0 < x < π/2. From the above, can we conclude that 0 < sin (x/2) < x/2? How about 0 < sin (x/5) < x/5? Why? How about 0<sin 3x < 3x ? Why?

Would you mind explaining how the electrons flow in the circuit & how the current flows in the circuit?

When the emitter is connected to the positive polarity of a battery, it is said that 'Some high speed electrons are still able to reach the collector and therefore there is flow of current.' (1) What is the flow of electrons like in this case? I thought electrons are supposed to flow from...

I think if you draw a free body diagram for a coil in the middle and another one for the coil near the wall, you may find that the sum of the tensions (the pulling force that acts on the coil) for the coil near the wall is greater than the sum of tensions that pulls the coil in the middle...

Thanks for the explanation which I cannot find anywhere. Thanks to everyone who replied to my post.

Do you mean spring force or normal force or both as the force on the book exerted by the spring on the book?[/COLOR]

If there is no platform, just the book on the spring, will there still be a normal force on the book other than spring force and the weight of the book?

Perpendicular

Homework Statement A vertical spring is fixed on a table. A book is put on the spring. The book compresses the spring until static equilibrium is reached. Question: Is there a normal force exerted by the spring on the book? Why or why not? Homework Equations The Attempt at a...

When r approaches zero or when they are very close to one another, the gravitational force is as large as the electrical force. Both the forces approach infinity. or When r approaches infinity or when they are very far apart, the gravitational force and the electrical force approach zero. Make...

You're good. You can see the different reference frames and introduce relative velocity.

What you said is very true.

square root of [2mgh/(M+m)]?

Thanks for explaining, again.

Let say I have a spring with spring constant of 10 N/m. I compress both ends with the same force so that each end compresses by 5 cm. Thus, the total compression is 10 cm. If I use F=kx where x is the total compression, then the spring force acting on each of my hand is 1 N. If I use F=kx...

Thank you for your insight.

1. Are the spring forces at both ends of a spring always equal in magnitude? 2. If yes, then the external forces at both ends are also the same in magnitude, aren't they? (Based on Newton's third law) If no, how to find the two different spring forces at each of the end? 3. If the...

I have done some reading to find the answer. This is what I got: 1. Work-energy theorem applies only to particles. 2. Objects subject to friction cannot be treated as particles. 3. Thus it is wrong to apply work-energy theorem to objects subject to friction.

If we include heat in the equation, how will it fix the equation? Or if the table is free to move, then it will move and gain kinetic energy of 1 J?

So, the table should move to fix the -1 = 0?

A block (2 kg) is moving with an initial speed of 1 m/s on a horizontal rough table comes to a stop eventually. Applying work-energy theorem to the block-table system, we obtain Change in the kinetic energy of the block + Change in the kinetic energy of the table = Net work done on the...

Homework Statement When a block is dropped to a disc that is rotating with a constant angular velocity about its centre, at the end, we know that both of them will rotate with the same new angular velocity which is slower than the previous one. Question: What is the force that makes the...

Thank you for your input.

I know that s is the displacement of the body, not the force. Whether there are 2, 3 or 10 forces acting on the body, the body will only move in one direction and therefore one displacement. Thus, when we find the work done by each of the force, we use the same s, the displacement of the body.

Net work done on a body = (F1 dot s) + (F2 dot s) + (...) = (F1 + F2 + ...) dot s = (Net force) dot s = Work...

I know that the net work done on a body equals to the sum of the work done by each of the forces acting on the body which also equals to the work done by the net force acting on the body. I can't see the whole picture. I don't get the same thing when I view it from different angles. Something...

Then force D will do some work on the spring since the point of application is moving because this end of the spring is oscillating together with the mass. So, there will be a net work done on the spring. Force E does zero work on the spring while force D does some work on the spring. So, there...

No. I just wondered when I read a book and did some exercises.

The net work done on the wall for sure is zero. Is there any relationship between the work done on the wall with the work done on the spring by the wall? I do not know anything about that.

The wall is not moving. Its displacement is zero. Force E is exerted on the spring by the wall.

When the spring is compressed, that force is a push. When spring is stretched, that force is a pull.

Let say we have a horizontal mass-spring system oscillates without friction on a smooth surface. One side of the spring is attached / fixed to a wall. The other is where the mass is attached to. Let say we choose our system to be the mass and the spring (negligible mass), so our free body...

sorry. you're right all this while.

yes. you're right. cot (3pi/2) is not undefined. it is 1/undefined.

i don't think it is right to say that 1/undefined = 0.

When i substitute pi/2 into the original equation, cot 3x will be undefined. Can we take pi/2 as a solution?

Words have spreaded

Coordinate geometry

1. A(0,0); B(a,0); C(0,a), M(0,a/2). 2. Slope of MB = -1/2 3. Slope of AP = 2 4. Equation of AP: y = 2x 5. Equation of CB : y = -x + a 6.Intersection of AP & CB is P(a/3, 2a/3). 7. BP: PC = 2:1.

If the tire makes 1 revolution, the car has traveled for a distance corresponds to 1 revolution. If the tire makes 2 revolution, the car has traveled for a distance corresponds to 2 revolutions. If the tire 17.4 revolutions in 1 second, what is the distance traveled? How much time is needed...

Perhaps you should consider the air resistance (the drag force) and the friction to come out with a reasonable explanation that is consistent with your data.

no it is wrong too.

i think u will just have to wait.

you can't. only the moderators can.

figure attached.

find the inverse tangent is right. the two values are wrong and irrelevant.

I would try sketching a figure and locate the two given points on the figure. Draw the right triangle that is appropriate for figuring out the angle.