- #1
slambert56
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I am new here so if any other info is needed lmk.
Ok I have been working on this problem for a very long time and there is a possibility that my book's answer is wrong. If that's the case I am going to be very mad ahaha. I put up the diagram and my work is after the passage. I don't think my logic is wrong but I might have missed something.
http://img196.imageshack.us/img196/5859/mmspicture8o.jpg
The block on the left ledge is 10.0kg and the block on the right is 3.00kg.
Uploaded with ImageShack.us
In the drawing, the rope and the pulleys are massless, and there is no friction. Find a) the tension in the rope and b) the acceleration of the 10kg block. (Hint: theh larger mass moves twice as far as the smaller mass) The books answer is a) 13.7N and b) 1.37m/s^2.
I am not worried about answer b, because I can't get the first part!
(m1) mass 1=10kg (m2)mass2=3kg
g=gravity 9.8
a=acceleration
Heres my work.
Ok so since there is no friction the 10kg block's only forces are the weight pointing down 10kg*9.8m/s^2=98N and its going to have positive acceleration to the right.
equation 1: for 10kg block is just T(tension)=m1*a
Now the fun begins with the 3kg block. Now originally I didn't catch that there must be 2 tensions because 2 ropes are attached to the 3kg box. All the 3 tensions should be the same force. The acceleration is negative since its going down.
This is probably where there could be a mistake. Should I add mass 1 and 2 in 3kg equation or just have m2
For 3kg there is only movement in y-axis so equation 2 is: 2T-m2*g=-a(m1+m2)
Then i add in equation 1 from 10kg into equation 2.
2(m1*a)-m2*g=-a(m1+m2)
2(m1*a)+a(m1+m2)=m2*g
a(2*m1+m1+m2)=m2*g
a=m2*g/(3*m1+m2)
a=3kg*9.8m/s^2 / 3*10kg+3kg
a=.891m/s^2
plug into equation 1 to solve T. T=m1*a T=8.91N
Now I tried various methods which usually works but I have tried everything and can't get 13.7N I also tried not including mass1 in the second equation and i still get a different answer.
2T-m2*g=-a(m2)
a=m2*g/(2*m1+m2)
a=3kg*9.8m/s^2/2*10kg+3kg
a=1.28m/s^2
plug in for t and get T=12.8N
Now I thought 12.8 could possibly be it due to imprecision but I used 4 sig figs then rounded to 3sig figs so it is not imprecise.(I hate sig figs)
I assume all the tensions will be same because if they are different I can't solve because there aren't enough variables. Thanks for any help or guidance. I am going to sleep soon but I will be on here tomorrow morning. Now if the accelerations are different, even when i plug them in how can i solve to get an acceleration?
After I solve this my life will be complete...
Ok I have been working on this problem for a very long time and there is a possibility that my book's answer is wrong. If that's the case I am going to be very mad ahaha. I put up the diagram and my work is after the passage. I don't think my logic is wrong but I might have missed something.
http://img196.imageshack.us/img196/5859/mmspicture8o.jpg
The block on the left ledge is 10.0kg and the block on the right is 3.00kg.
Uploaded with ImageShack.us
Homework Statement
In the drawing, the rope and the pulleys are massless, and there is no friction. Find a) the tension in the rope and b) the acceleration of the 10kg block. (Hint: theh larger mass moves twice as far as the smaller mass) The books answer is a) 13.7N and b) 1.37m/s^2.
I am not worried about answer b, because I can't get the first part!
(m1) mass 1=10kg (m2)mass2=3kg
g=gravity 9.8
a=acceleration
Heres my work.
Ok so since there is no friction the 10kg block's only forces are the weight pointing down 10kg*9.8m/s^2=98N and its going to have positive acceleration to the right.
equation 1: for 10kg block is just T(tension)=m1*a
Now the fun begins with the 3kg block. Now originally I didn't catch that there must be 2 tensions because 2 ropes are attached to the 3kg box. All the 3 tensions should be the same force. The acceleration is negative since its going down.
This is probably where there could be a mistake. Should I add mass 1 and 2 in 3kg equation or just have m2
For 3kg there is only movement in y-axis so equation 2 is: 2T-m2*g=-a(m1+m2)
Then i add in equation 1 from 10kg into equation 2.
2(m1*a)-m2*g=-a(m1+m2)
2(m1*a)+a(m1+m2)=m2*g
a(2*m1+m1+m2)=m2*g
a=m2*g/(3*m1+m2)
a=3kg*9.8m/s^2 / 3*10kg+3kg
a=.891m/s^2
plug into equation 1 to solve T. T=m1*a T=8.91N
Now I tried various methods which usually works but I have tried everything and can't get 13.7N I also tried not including mass1 in the second equation and i still get a different answer.
2T-m2*g=-a(m2)
a=m2*g/(2*m1+m2)
a=3kg*9.8m/s^2/2*10kg+3kg
a=1.28m/s^2
plug in for t and get T=12.8N
Now I thought 12.8 could possibly be it due to imprecision but I used 4 sig figs then rounded to 3sig figs so it is not imprecise.(I hate sig figs)
I assume all the tensions will be same because if they are different I can't solve because there aren't enough variables. Thanks for any help or guidance. I am going to sleep soon but I will be on here tomorrow morning. Now if the accelerations are different, even when i plug them in how can i solve to get an acceleration?
Homework Statement
After I solve this my life will be complete...
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