Angular acceleration, velocity, momentum of a door?

In summary: I can't find that.e) Combining angular acceleration and linear acceleration considerations, findthe tangential force Fh supplied by the hinges as a function of d, the distancebetween the hinges and the point of application of the mother-in-law force(d was l=2 in part a) and b), and l in part c); now use a general d). Don’tput in explicit numbers, just find the equation.f) For which d do the hinges not need to provide any tangential force?The Attempt at a Solution Can someone check on my solutions, All answers appreciated![/B]a)τ= l/
  • #1
Haveagoodday
43
1
Skjermbilde 2015-10-29 kl. 21.45.27.png


1. Homework Statement

A door of width l = 1.00 m and mass M = 15.0 kg is attached to a door

frame by two hinges. For this problem, you may ignore gravity, as we are

interested in rotational motion around the vertical axis. There is no friction

of any kind.

An angry mother-in-law slams the door shut, by pushing at the middle of

the door (l=2 from the hinges) with a force of F = 100N, lasting a time

t = 0:.00 s. The door is initially not rotating. The door can be taken to be

a uniform rod, for the purpose of this exercise.

a) What is the angular acceleration of the door while it is being pushed?

b) What is the resulting angular velocity, angular momentum and rotational

kinetic energy from this push?
c) Assuming that she let's go of the door (leaving it to slam shut) at the

moment in the motion when the door is perpendicular to the wall, how long

does it take for the door to close?

d) What would be the result of a), b), c) and d) if she had pushed not in the

middle of the door but at the edge (l from the hinges)?

In addition to the force of the mother-in-law, the hinges also provide force,

both radial (centripetal) and tangential force while the mother-in-law pushes

(they also compensate for gravity to keep the door upright, but ignore that

for now).

e) Combining angular acceleration and linear acceleration considerations, find

the tangential force Fh supplied by the hinges as a function of d, the distance

between the hinges and the point of application of the mother-in-law force

(d was l=2 in part a) and b), and l in part c); now use a general d). Don’t

put in explicit numbers, just find the equation.

f) For which d do the hinges not need to provide any tangential force?

The Attempt at a Solution


Can someone check on my solutions, All answers appreciated![/B]
a)
τ= l/2*F=50
τ=M*(l/2)^2*α
α=τ/M*(l/2)^2= 13.33 rad/s^2

b)
ω=ωi+αt=2.7 rad/s
I=(1/12)*Ml^2=1.25 kg*m^2
L=I*ω=3.375 kg*m^2/s
K=(1/2)*I*ω^2=4.56 J

c)
θ=θ+ωt+(1/2)αt^2
π/2=2.7t+(1/2)13.33t^2
used the abc rule
t=0.323 s
d)
τ= l*F=100
τ=M*l^2*α
α=τ/M*l^2= 6.7 rad/s^2

ω=ωi+αt= 1.34 rad/s
I=(1/3)*Ml^2=5 kg*m^2
L=I*ω=6.7 kg*m^2/s
K=(1/2)*I*ω^2=4.489 J

θ=θ+ωt+(1/2)αt^2
π/2=1.34t+(1/2)6.7t^2
used the abc rule
t=0.512 s


e)
This solution i am sure is wrong
Fh(d)= τ(d)/I + F(d)/M

d)
d=l
 
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  • #2
Haveagoodday said:
View attachment 91039

1. Homework Statement

A door of width l = 1.00 m and mass M = 15.0 kg is attached to a door

frame by two hinges. For this problem, you may ignore gravity, as we are

interested in rotational motion around the vertical axis. There is no friction

of any kind.

An angry mother-in-law slams the door shut, by pushing at the middle of

the door (l=2 from the hinges) with a force of F = 100N, lasting a time

t = 0:.00 s. The door is initially not rotating. The door can be taken to be

a uniform rod, for the purpose of this exercise.

a) What is the angular acceleration of the door while it is being pushed?

b) What is the resulting angular velocity, angular momentum and rotational

kinetic energy from this push?
c) Assuming that she let's go of the door (leaving it to slam shut) at the

moment in the motion when the door is perpendicular to the wall, how long

does it take for the door to close?

d) What would be the result of a), b), c) and d) if she had pushed not in the

middle of the door but at the edge (l from the hinges)?

In addition to the force of the mother-in-law, the hinges also provide force,

both radial (centripetal) and tangential force while the mother-in-law pushes

(they also compensate for gravity to keep the door upright, but ignore that

for now).

e) Combining angular acceleration and linear acceleration considerations, find

the tangential force Fh supplied by the hinges as a function of d, the distance

between the hinges and the point of application of the mother-in-law force

(d was l=2 in part a) and b), and l in part c); now use a general d). Don’t

put in explicit numbers, just find the equation.

f) For which d do the hinges not need to provide any tangential force?

The Attempt at a Solution


Can someone check on my solutions, All answers appreciated![/B]
a)
τ= l/2*F=50
τ=M*(l/2)^2*α
α=τ/M*(l/2)^2= 13.33 rad/s^2

b)
ω=ωi+αt=2.7 rad/s
I=(1/12)*Ml^2=1.25 kg*m^2
L=I*ω=3.375 kg*m^2/s
K=(1/2)*I*ω^2=4.56 J

c)
θ=θ+ωt+(1/2)αt^2
π/2=2.7t+(1/2)13.33t^2
used the abc rule
t=0.323 s
d)
τ= l*F=100
τ=M*l^2*α
α=τ/M*l^2= 6.7 rad/s^2

ω=ωi+αt= 1.34 rad/s
I=(1/3)*Ml^2=5 kg*m^2
L=I*ω=6.7 kg*m^2/s
K=(1/2)*I*ω^2=4.489 J

θ=θ+ωt+(1/2)αt^2
π/2=1.34t+(1/2)6.7t^2
used the abc rule
t=0.512 s

e)
This solution i am sure is wrong
Fh(d)= τ(d)/I + F(d)/M

d)
d=l
It appears that you have some typos in the statement of the problem

I assume she pushes the door at a point located L/2 from the axis of rotation. (Lower case L should be banned as a variable.)

The time interval over which she pushes is not given. It looks like you used t = 0.20 seconds.

What did you use for the moment of inertia of the door ?
 
  • #3
SammyS said:
What did you use for the moment of inertia of the door ?
... and about what axis?
Haveagoodday, you seem to have used ML2/4 in a) and ML2/12 in b).
 
  • #4
I have same answers in a and b, but you have a typo in b. In c you have to calculate again, your answer is wrong.
 
  • #5
coffeemanja said:
I have same answers in a and b,
None of the answers given to a) and b) in the OP are correct.
 
  • #6
And why is that so? My only guess is that I should take Fsin0 instead of pure F... Then it will change all the answers
 
  • #7
Wait, it will not change a thing.
 
  • #8
A) ΣFt=mat->at= ΣFt/m=6,7
α=at/r=6,7/0,5=13,4
Where did I go wrong?
 
  • #9
at is tangential acceleration
 
  • #10
coffeemanja said:
And why is that so? My only guess is that I should take Fsin0 instead of pure F... Then it will change all the answers
My guess is that haruspex did not guess.
 
  • #11
coffeemanja said:
A) ΣFt=mat->at= ΣFt/m=6,7
α=at/r=6,7/0,5=13,4
Where did I go wrong?
This is rotation. Use torque and moment of inertia.
 
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  • #12
haruspex said:
This is rotation. Use torque and moment of inertia.
Now I got 40 in a.
 
  • #13
coffeemanja said:
Now I got 40 in a.
Better, but as Sammy pointed out in post #2 the L=2 must be a typo, probably for L/2. Does that change your answer?
 
  • #14
haruspex said:
Better, but as Sammy pointed out in post #2 the L=2 must be a typo, probably for L/2. Does that change your answer?
L/2 is correct. And that is what I used.

All answers are new and angry mother-in-law is slaming the door faster, when she holds at the edge. Seems reasonable.
But I'm so stuck at e) now...
 
  • #15
coffeemanja said:
L/2 is correct. And that is what I used.
Then you are probably using the wrong moment of inertia formula. What did you use?
coffeemanja said:
All answers are new
Would you like them checked?
coffeemanja said:
But I'm so stuck at e) now...
How far do you get? What equations do you have?
 
  • #16
coffeemanja said:
Now I got 40 in a.
 
Last edited:
  • #17
haruspex said:
Then you are probably using the wrong moment of inertia formula. What did you use?

Would you like them checked?

How far do you get? What equations do you have?

i now got 40 in a
and 8 rad/s, 10 kgm^2/s, 40J in b
are these answers correct?
And what equations can i use in c?
 
  • #18
Haveagoodday said:
i now got 40 in a
As I implied in post #15, I get a different answer. Please post your working.
 
  • #19
coffeemanja said:
I have same answers in a and b, but you have a typo in b. In c you have to calculate again, your answer is wrong.
how did you calculate c?
 
  • #20
haruspex said:
As I implied in post #15, I get a different answer. Please post your working.
in a:
I=Ml^2/12=1.25
α=T/I=40
in b:
w=w+αt=8
L=Iw=10
K=Iw^2/2=40
 
  • #21
Haveagoodday said:
how did you calculate c?
Coffeemanja should not lay out the solution for you.
What is the acceleration in part c?
 
  • #22
Haveagoodday said:
in a:
I=Ml^2/12=1.25
Where is the axis of rotation?
 
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  • #23
j
 
  • #24
haruspex said:
Coffeemanja should not lay out the solution for you.
What is the acceleration in part c?
I don't want him to give me the solution, i calculated the problem and i got a wrong answer, all i want is just a tip.
 
  • #25
haruspex said:
Where is the axis of rotation?
is it the y axis, or?
 
  • #26
Haveagoodday said:
is it the y axis, or?
Where is it in relation to the door?
 
  • #27
haruspex said:
Where is it in relation to the door?
it is in relation to the height of the door?
 
  • #28
Haveagoodday said:
it is in relation to the height of the door?
No, it's vertical. In relation to the width.
 
  • #29
haruspex said:
No, it's vertical. In relation to the width.
Ok, but how does that make my result wrong?
 
  • #30
Haveagoodday said:
Ok, but how does that make my result wrong?
You're not answering my question. Where is this vertical axis in relation to the door's width? Does it run up the middle of the door?
 
  • #31
haruspex said:
You're not answering my question. Where is this vertical axis in relation to the door's width? Does it run up the middle of the door?
I got 10 in a)...Inertia formula that i have used is: I=(ML^2)/3...The question says that we should consider the door as a uniform rod, hence the formula that i have chosen to use...Please correct me if I'm wrong
 
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  • #32
StavangerFinest said:
I got 10 in a)...Inertia formula that i have used is: I=(ML^2)/3...The question says that we should consider the door as a uniform rod, hence the formula that i have chosen to use...Please correct me if I'm wrong
That's it.
 
  • #33
haruspex said:
That's it.

I'm a bit stuck with e) though, I get tangential force to be Ft= ((mr^2α)/d)-mrω^2-F (the force from the mother-in-law which is 100N), and it doesn't seem like the correct answer.
Guidance or any tip is appreciated
 
  • #34
haruspex said:
That's it.
 
  • #35
On c.) could the time be 2,53s (also got t= -1,26), used abc formula with α=10 and ω=2? Used the inertia formula that StavangerFinest did: I = (ML^2)/3.
 
<h2> 1. What is angular acceleration? </h2><p> Angular acceleration is the rate of change of angular velocity with respect to time. It is a measure of how quickly the rotational speed of an object is changing. </p><h2> 2. How is angular acceleration calculated? </h2><p> Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. It is represented by the symbol alpha (α) and is measured in radians per second squared (rad/s^2). </p><h2> 3. What is angular velocity? </h2><p> Angular velocity is the rate of change of angular displacement with respect to time. It is a measure of how fast an object is rotating around a fixed axis. </p><h2> 4. How is angular velocity related to linear velocity? </h2><p> Angular velocity and linear velocity are related by the distance from the center of rotation. The linear velocity is equal to the angular velocity multiplied by the radius of the circle. This relationship is known as the tangential velocity. </p><h2> 5. What is the momentum of a door? </h2><p> The momentum of a door is the product of its mass and linear velocity. It is a measure of the amount of motion the door has and is conserved in a closed system. The angular momentum of the door can also be calculated by multiplying its moment of inertia by its angular velocity. </p>

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity with respect to time. It is a measure of how quickly the rotational speed of an object is changing.

2. How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. It is represented by the symbol alpha (α) and is measured in radians per second squared (rad/s^2).

3. What is angular velocity?

Angular velocity is the rate of change of angular displacement with respect to time. It is a measure of how fast an object is rotating around a fixed axis.

4. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related by the distance from the center of rotation. The linear velocity is equal to the angular velocity multiplied by the radius of the circle. This relationship is known as the tangential velocity.

5. What is the momentum of a door?

The momentum of a door is the product of its mass and linear velocity. It is a measure of the amount of motion the door has and is conserved in a closed system. The angular momentum of the door can also be calculated by multiplying its moment of inertia by its angular velocity.

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