Help I made a physics problem for a project

[Scott_j]

Homework Statement

I made a physics problem for a project that we had to do, but I do not know where to start.

Saruman’s plan to get the one ring involves disposing of the ring-bearer. To protect Frodo, Gandalf fights Saruman. In the following battle, Saruman pushes Gandalf 20 feet across the floor at a speed of 60 m/s. Before he hits the window, 8 foot fall Gandalf plants his staff into the ground which causes him to rotate around it.a) Determine the torque of gandalf as he rotates on his staff for 8 seconds if he weighs 120 kg.Saruman then throws a large book with a mass of 18.0 kg at gandalf who is then thrown out the window.b) What is his momentum before he hits the window and after he falls through, if the window falls along with gandalf, given that the mass of the window is 20 kg?c) What is the distance Gandalf is thrown out the window when he reaches the ground?

Homework Equations

ω=v/r
I=mr^2
Torque=I*α
KE=1/2Iω^2, [/B]

The Attempt at a Solution

This problem involves many things, and I don't know where to start.

 

[haruspex]

Unfortunately, your not knowing where to start is reflected in what you have asked. The question does not actually make sense. E.g. why should there be any torque on Gandalf just because he is spinning around his staff? What is the consequence of torque on a rotating body?

 

[Scott_j]

Forgot to add in this part: Saruman is constantly applying a force to gandalf's feet to make him rotate continously, so when the block hits him, some of the kinetic energy of the book is shared with rotational energy of gandalf.

 

[haruspex]

Forgot to add in this part: Saruman is constantly applying a force to gandalf's feet to make him rotate continously, so when the block hits him, some of the kinetic energy of the book is shared with rotational energy of gandalf.

Why was a force needed to keep Gandalf rotating?

 

[Scott_j]

I rewrote the question, ill write it in a second, thanks for responding though. . . Its 4 am right now and the thing's due in couple hours.

 

[Scott_j]

1. Saruman’s plan to get the one ring involves disposing of the ring-bearer. To protect Frodo, Gandalf fights Saruman. In the following battle, Saruman tosses Gandalf 20 feet across the room at a speed of 10 m/s. Before he falls out of the 138 meter tall tower, Gandalf plants his staff into the floor which causes him to rotate.. He then uses his powers to gradually bring his rotation to a stop.

a) Calculate the angular velocity of Gandalf as he rotates around his staff before he stops, if he is 2.5 meters tall. Gandalf then slows himself down at a rate of -0.5 rad/s^2. How long does it take for him to slow down completely?

Before Gandalf has a chance to recover, Saruman throws a large rock with a mass of 140.0 kg at gandalf at a speed of 20 m/s, who is then thrown out a open window.

b) What is his momentum of the system before and after it hits gandalf? What is the velocity of Gandalf as he is thrown out the window?

c) What is the distance Gandalf is thrown out the window when he reaches the ground?

I rewrote these to be a lot easier. .
a) w/=v/r
w=10/2.5
w=4 rad/sec

w(final)=w(initial)t + α
t=(w-w(initial))/α
t=(0-4)/-0.5=6 seconds

b)Momentum of rock: p=mv p=(140kg)(20m/s) p=2800
Momentum of Gandalf: p=mv p=(120kg)(0m/s) p=0

p(total)=p(total,final)
m1v1+m2v2=m1fv1+m2fv2
m1v1=(m1+m2)*v(final)
2800=(260)*v(final)
v(final)=10.76m/s

c) y represents the vertical axis, x represents horizontal

dy=1/2at^2+v(initial)y
138=1/2(-0.8m/s^2)(t^2)
t=sqrt(2(138)/9.8))
t=6.969

dx=1/2at^2 +v(initial)*t
dx=v(initial)(6.969)
dx=10.76(6.969)
dx=74.98 meters

 

[haruspex]

That works much better as a question.
Your answer to a) is wrong. You can't assume the rotation rate will be his prior speed divided by the radius. You need som physical law you can invoke. What conservation law might help?
I'll post this and continue reading your answers.

 

[Scott_j]

Im basing letter a on that gandalf is rotating 0.63 rev/sec, multiplied by 2pi to get 4rad/sec.

 

[haruspex]

A) ctd. -4/-.5 = 6??
B) you didn't specify a mass for Gandalf in the question. I gather it's 120kg.
C) you have a number of typos, and looks like a numerical error in the last step of finding t. Check that again.

 

[Scott_j]

Oh yes thanks for pointing out the errors, for a) i mistakenly thought that 0-4 was 1-4 for some reason.

 

[haruspex]

Im basing letter a on that gandalf is rotating 0.63 rev/sec, multiplied by 2pi to get 4rad/sec.

No you didn't, you divided 10m/s by 2.5 m, but it's wrong either way. If did get .63 rev/s by some other route, how did yiu get it?

 

[Scott_j]

I worked backwards, so that I calculated angular velocity from 10 m/s.
w(initial)=0.63 rev/s = 2pi(0.63)rad/s = 4 rad/s
v=r*w=2.5(4)=10m/s

 

[haruspex]

I worked backwards, so that I calculated angular velocity from 10 m/s.
w(initial)=0.63 rev/s = 2pi(0.63)rad/s = 4 rad/s
v=r*w=2.5(4)=10m/s

As I keep trying to tell you, you cannot calculate his angular speed that way. You are assuming that after grabbing his staff his feet continue to move at 10m/s. You cannot assume that.
Name some conservation laws.

 

[Scott_j]

F=ma
Torque=I*angularacceleration

 

[haruspex]

F=ma
Torque=I*angularacceleration

They are not conservation laws.

 

[Scott_j]

KE=1/2Iw^2...
Please forgive me if I'm not getting it, it's nearly 5 am and I haven't gotten any sleep

 

[haruspex]

KE=1/2Iw^2...
Please forgive me if I'm not getting it, it's nearly 5 am and I haven't gotten any sleep

Do you really not know any conservation laws? Energy? Momentum? Angular momentum?

 

[Scott_j]

yea L=Iw
gpe=ke. . .

 

[haruspex]

yea L=Iw
gpe=ke. . .

You're not getting there. Look up conservation of angular momentum.

 

[Scott_j]

L = mvr m is the mass of the object, v is the magnitude of its velocity, and r is the separation between the objects.

 

[haruspex]

L = mvr m is the mass of the object, v is the magnitude of its velocity, and r is the separation between the objects.

That's a formula for assessing angular momentum in certain situations (which need to be quoted or the formula means nothing), but it is not a conservation law. After you have found out what conservation of angular momentum says, you will need to be able to quote the moment of inertia of a rod (being the nearest simple shape for Gandalf). Can you do that?