My high school physics teacher had all sorts of quiz questions involving disgruntled people throwing keys, cars, refrigerators, etc off cliffs and out windows. I even remember a question about a guy standing on the back of a truck in an "ideal world" who shoots an arrow straight up while the truck is moving, and asking where the arrow landed.
I think this is a trick question? The scale should read the same. I've been out of school too long to do the math. Cheers.
I hope they took into account that hamsters have claws and depending upon the softness of the wood he is sitting on, the hamster may never slide down.
Though, should the hamster get tired of waiting and take a weee & a dump, the extra lubricant flowing downhill under his paws might force the hamster down the block anyways. ;)
Oh and should this be a male hamster and he sense a female hamster at the bottom of the block in heat, his desire might force him to run down the ramp! GROWL!
Of course as the male hamster just gets to the bottom a cat comes by and both the male and female hamster run up the block and jump off the top to scurry away!
"...it's more fun if we have an actual hamster, some lube..."
"but it's more fun if we have an actual hamster, some lube, and an inclined block"
Thats sick and twisted, and not at all nice to the hamster!
I think it should be:
Is this correct?
About 9.34N if my equation is correct.
I would suggest the following equation:
[(1-sin(theta))*200g] + 800gr. Where theta is the angel of the incline.
The reasoning behind the equation is the following: there are two limiting cases
1) The angel is zero and the full weight of the movable object ( in this case the hamster) is resting on the block. Sin(0) = zero and so the first term in the equation is 200gr
2) The angle is 90 degrees and the hamster is in free fall and thus no weight is being exerted by it on the block. Sin(90) = 1, 1-1 = 0 and thus the first term goes to zero in this situation.
At 40° the sliding hamsters would register a weight of 71.4 gr. thus making the total system weight 871.4gr.... 1000gr. = 9.8 N; 871.4gr = approximately 8.54N
The same argument can be made for my equation.
Cos(0) = 1
Cos(90) = 0
I debated between the two equations and did not know which one was correct. What other reasoning influenced you to use the equation you presented?
The force that is of interest (the force applied by the hamster due to the influence of gravity) is in the negative Y direction. The way that the drawing is constructed, this can be expressed through the sin of the given angle.
You are correct in that the cos also has the limits of 1 and 0 at zero and 90 degrees, but this function relates the hypotenuse of the right triangle to its projection along the X direction…perpendicular to the direction of the force that is of interest.
The equation can also be expressed using a cosine of the opposite angle (90-theta), in this case, the cosine of 50.
1-cos(50) = 1- sin(40)
Luke, may the force of the great Hamster be with you.
~ Obi-Wan Kenobi
I checked with all my friends and a few websites and they all agree with me. The one architect I checked with said that if the sine cosine relationship was linear your approach would work but the trade off is non-linear. If the 0 friction lube eliminates the parallel to the inclined plane component of the gravitational force acting on the scale and wedge then only the perpendicular component is left. The formula for perpendicular component is the one I used above.
The cos function of the given angel has the correct limits but why I am hesitant to agree is that the gravitational force is in the y direction and the cos function is a projection perpendicular to it.
I could be wrong in this though.
The question is, would numbers for the weight predicted by the cos function fit data points from an experiment in between the limits? Lacking an experimental set up to test this, I will copy the problem and take a walk over the physics department and ask there.
Stay tuned for the exciting continuation of the Case Of The Sliding Hamster…
“Sine here on the dotted line”
“Cos I want to do it the other way”
This is a bit dumb...the reading on the scale would not change , the combined mass of the hamster and block is still the same.
Rather than sliding a hamster down a block; I find it a lot more interesting to launch a hamster into space!
Hey Robot, you get the the liquid oxygen and I will get the hampster
Don't forget, the movement still has a vector.
The animal welfare people misunderstood when they heard I was lubing up a hamster for an experiment. Could I call you as witnesses?
matsci1 & Braggston,
Sine and Cosine represent ratios and I don't think that using their complement is legitimate. If you want to do a proper vector analysis of this problem then look at the angle between the vertical force vector and the incline surface. That is 50 degrees. Now you use the Sine to find the vertical component. It is the same as the Cos of the angle to the horizontal. Make sense?