Physics help needed...

[magdalena]

Hello everyone,
I am taking physics I and I simply struggle with it. Last time I got great help from Scrumhalf. Unfortunately, many of the things are still little unclear to me, I am able to set up the problem but I get stuck in the middle, so please, any input is welcomed.
The problems should be solved with either 1-D or 2-D kinematics equations. And they are as follow:

1. A force, F1, of magnitude 2.0 N and direction due east is exerted on an object. A second force exerted on the object is F2= 2.0 N, due north. What is the magnitude and direction of a third force, F3, which must be exerted on the object so that the resultant force is zero?

2. A turtle takes 3.5 minutes walk 18 m toward the south along a deserted highway. A truck driver stops and picks up the turtle. The driver takes the turtle to a town 1.1 km to the north with an average speed of 12 m/s. What is the magnitude of the average velocity of the turtle for its entire journey?

3. A tennis ball is thrown from ground level with velocity v(o) directed 30'(degrees) above the horizontal. If it takes the ball 1.0s to reach the top of its trajectory, what is the magnitude of the initial velocity?

[Scrumhalf]

1. It is important to remember that force is a vector, i.e. it has magnitude and direction.

So, if I assume that the unit vector in the east direction is i and the unit vector in the north direction is j, the force that is being applied is 2i + 2j.

Since force has direction, you can't simply add up the 2 numbers and say that the net force on the object is 4N. That would be wrong because the 2 forces are not in the same direction. You can only add numbers in the same direction.

The way to compute the magnitude of a vector is to add the two numbers in quadrature, i.e the total force is the square root of the sum of the squares of the 2 forces.

That is, the net force is sqrt (2^2 + 2^2), i.e. sqrt(8) = 2.83N

In this particular problem, the direction of the force is easy because the 2 forces are equal. Since there is a 2N force due east and another 2N force due west, the net force is going to push the object halfway between north and east, i.e in the north-easterly direction.

So, if you need to make the resultant force on the object to be zero, you need to apply a force of 2.83N due south-west to counteract the other two forces.

It is crucial that you learn about vectors to do these kinds of problems. Knowing how to add vectors and compute magnitude and direction of vectors is a key requirement for being able to do these kinds of kinematics problems. You might want to get a professor or teaching assistant to sit down with you and show you how to compute vectors.

It is a bit hard to do over the web. I'll see if I can find some sites or book references to post but it is probably a lot easier to do in person.

[Scrumhalf]

2. The turtle traveled 18m south by itself and then 1100m east on the truck.

So, the total distance it goes is sqrt (18^2 + 1100^2) = 1100.15m

(It might be instructive to draw a picture here. 18m and 1100m represent 2 sides of a right-angled triangle. The hypotenuse is the total distance traveled which I computed above using the Pythagorean Theorem).

The truck driver went at 12m/sec to go 1100m, i.e. he took 1100/12 = 91.67sec to complete his portion of the trip. So, the total time the turtle traveled = 3.5min + 91.67sec = 210 + 91.67 = 301.67sec. So, the turtle went 1100.15m in 301.67 sec, i.e at a speed of 3.65 meters/sec.

[blm]

Looks like we a have a resident Physics professor now. Twice in a week, lol.

[Scrumhalf]

3. For this problem, you need to use some trigonometry.

The velocity v0 is directed at 30 degrees above horizontal. So, the ball goes both vertically upwards and horizontally forwards.

What you need to find first is what fraction of the velocity makes the ball goes vertically upwards.

Imagine that the velocity v0 is like the hypotenuse of a triangle - it is the vector sum of a vertical velocity v_vert and a horizontal velocity v_horiz. Since v0 is at an angle of 30degrees to the horizontal,

sin (theta) = v_vert/v0.

Since theta = 30degrees, sin(30) = 0.5. That is, v_vert is half of v0.

Now, you need to use one of the equations from last time to compute what v_vert is and then you'll know what v0 is.

Remember that v = u + a*t

Since v = final velocity = 0 and u = initial velocity = v_vert,

v_vert = -a*t.

a = -9.8m/sec^2 and t=1

So, v_vert = 9.8m/sec

and v0 = 2*v_vert = 19.6m/sec.

[coffee-guy]

What do you do for a living Scrumhalf? Does it pertain to physics or what? I remember you saying you wanted to do something involving it but realized in college you weren't cut out for it - what did you decide to do instead?

[coffee-guy]

Looks like we a have a resident Physics professor now. Twice in a week, lol.

I think this should teach us to watch less television and to read more books :D...

[Scrumhalf]

I am an engineer, working for a company involved in the design and manufacturing of computer chips.

When I was growing up, I really wanted to be a physicist, especially in astronomy, but in college, I realized that my physics, while reasonably competent, was not of the topnotch quality that I felt I would need to be a physicist or at least a really good one. So, I decided to go into engineering instead.

[coffee-guy]

I am an engineer, working for a company involved in the design and manufacturing of computer chips.

When I was growing up, I really wanted to be a physicist, especially in astronomy, but in college, I realized that my physics, while reasonably competent, was not of the topnotch quality that I felt I would need to be a physicist or at least a really good one. So, I decided to go into engineering instead.

Nothing to scoff at there my friend - I'm still trying to figure out what I want to be when I grow up :)

[magdalena]

Scrumhalf,
thank you again for your help.
However, in the second problem, the turtle was going south by himself and then was picked up by the driver and they went north. So in this case I know I cannot use the Pythagorean theorem since the directions overlap. I was trying to just get the average velocity and add them up but then dividing it by two probably wouldn't get me anywhere...
For the first one with adding vectors, I know it is easy to calculate this one but I need to show the work and use one dimension kinematics equation. I tried to get the x and y components but it seems that I don't have enough information to do it. I don't have an angle to calculate unless I assume that the angle is 90' (but then I am not sure if I could do that).
ANy ideas how can I fix that?

[Bouncer]

shibby, why arent you helping her with such simple problems bro? :D

[Scrumhalf]

OK.... it is important to distinguish between average speed and average velocity for problem 2. Speed is a scalar and velocity is a vector.

Average speed is the total distance travelled divided by the total time.

Average velocity is the total displacement from the original position to the final position divided by the time elapsed.

Total displacement from original position = 1100 - 18 = 1082m.
Time elapsed = 301.67 sec.
Average velocity = 1082/301.67 = 3.59 m/sec.

(Note that if the question asked for average speed, then you would have to do 1100 PLUS 18 divided by time elapsed, because speed is total distance traveled divided by time elapsed).

[Shibby]

shibby, why arent you helping her with such simple problems bro? :D

This work is too elementary to wast my time :D

[magdalena]

Thank you once again Scrumhalf.