Question

State the magnitude and direction of the total force on the object state the magnitude and direction of the total force on the object (puck, car, ball, or boat), how you determined your answer to 1, and
state whether the object will accelerate or not. If it does, in what direction will it accelerate?

Answer 1

I already turned this assignment in but it is open for revision since I did not receive a good grade on it. I am only stuck on these two questions, which I thought I would get right but my teacher keeps saying that they are wrong! Here are the questions: http://imgur.com/sG66wMH

Answer 2

I only got those two wrong and my responses are these:
For the boat, am I supposed to consider using the Pythagorean Theorem? a^2 + b^2 = c^2 // (length of one leg)^2 + (length of other)^2 = (length of hypotenuse)^2? OR d^2 = Δx^2 + Δy^2? I'll give the right triangle an angle of 90 degrees. Δx = 1000, Δy = 400
SO: d = 1000^2 + 400^2; d = 1000000 + 160000 = 1160000. I hope that's what you're looking for.

However, the teacher replied with this response:
The magnitude of the force is calculated using the correct process, but it is not finished. If you compare your answer to the original forces you should be able to see the mismatch. Should a force of 1000 N to the east and a force of 400 N to the north create a force of 1160000N to the NE? Seem a bit large to you?

What am I missing exactly?

Answer 3

And for the ball (which is what I'm having most troubles with) is this:
The Law of Inertia explains why an object at rest remains at rest. Although there is not an absence of a Net Force in this case, the ball is remaining at rest due to the law of Inertia. I'm only considering the two forces of the figures pushing against the ball. . This is where I'm lost. There is one figure pushing the ball right with a force of 150N, while there is another pushing to the left with a force of 90N. I'm not sure what you want me to decipher or figure out. . I thought these two forces and the sum of the two forces is what you were asking for.

Here is my teachers response:
What makes this different than the car in your mind? For the car you had opposing forces, calculated the total for, and stated it accelerated. Did it matter what the object was? Did it matter the nature of the forces? No. You calculated a total force. If the total is not zero, then the object accelerates. That is the beauty of N's 2nd law - simplicity.
A simple definition of acceleration is the rate at which velocity changes. Therefore if an object accelerates the velocity must change. OK, considering the two forces you are using, the 150N right and the 90N left, what is keeping you from stating the total force is 60 N to the right and the ball accelerates to the right? I'm trying to understand your difficulty with this since you have done the same process in the other examples.


What am I doing wrong? Any help would be greatly appreciate! :(

Answer 4

Firstly, for the boat, you were going in the right direction! I'm going to change your notation and verbiage a bit though - instead of saying the "length" of the leg, it's better convention to refer to each part of the Force vector as the "magnitudes" of the forces in a the directions East and North (Fe for the Eastern force and Fn for the Northern force), then the result you get from applying the Pythagorean Thm. will be the "resultant" force vector, Fr. Given those new definitions, the Pythagorean Thm leads to
\[|\textbf{F}_R|^2 = |\textbf{F}_E|^2 + |\textbf{F}_N|^2\]
which reads as "the square of the magnitude of the resultant force is equal to the square of the magnitude of the Eastern force plus the square of the magnitude of the Northern force. This is pretty much what you had above, but you forgot to take the square of the right hand side, which is why your teacher was saying that the force was pretty large (if both components are around 1000N, then the resultant force should be in that same order of magnitude - geometrically speaking, if you have a triangle with legs of 3 and 4, you wouldn't expect the hypotenuse to be 500!)

In any case, the above expression gives the magnitude of the resultant force to be
\[ |\textbf{F}_R| = \sqrt{|\textbf{F}_E|^2 + |\textbf{F}_N|^2}
\\ \
\\ =\sqrt{(1000N)^2 + (400N)^2}\]
To find its direction, you can refer to SOH-CAH-TOA, having both the opposite and adjacent components, giving the angle measured from the horizontal.
\[ \theta = \arctan \left( \frac{F_N}{F_E}\right)
\\ \
\\ =\arctan \left(\frac{400N}{1000N}\right)\]
\[ \textbf{F}_R = |\textbf{F}_R|\ \text{ at } \ \thetaº\]

Answer 5

I have one question for you about the ball - why are you assuming that the object is remaining at rest? This is the same question your teacher had.

Since there is a net force on the ball, the ball must be accelerating - the fact that the object is a ball has nothing to do with the fact that there is a net force acting on it, and because there is a net force, it is being accelerated in the direction of said net force. If we call the rightward for Fr acting in the positive x direction, and the leftward force Fl which is acting in the negative x direction, then noting that the forces are along the same line, the net force on the ball is given by
\[\textbf{F}_{net} = \textbf{F}_R + \textbf{F}_L
\\ \
\\ \textbf{F}_{net} = 150N - 90N\]

(We are ignoring the fact that it's a statue and isn't actually moving - we're imagining that the two dwarves are real, and that the ball is free to roll around ^_^ )

Holler if you have any questions about the help! ^_^

Answer 6

Thank you so much! So, for the boat, I would just have to take the square root? Is that all I was missing? What a simple mistake! So the answer would be 1077 N? :-)

Answer 7

Yup yup ^_^ Happy New Year!

Answer 8

:D Happy (late) New Years to you too!