What Is the Initial Acceleration of End B When the String Is Cut?

AI Thread Summary
The discussion focuses on calculating the initial acceleration of end B of a rod when the string supporting it is cut. The rod is 57.0 cm long and has a mass of 1.90 kg, with the string length being 41.0 cm. The user attempts to apply torque and Newton's laws but encounters confusion regarding the point of rotation and the application of the laws. Clarifications are sought regarding the center of mass and the correct interpretation of Newton's laws. The thread highlights the need for accurate calculations and understanding of rotational dynamics in this scenario.
Punchlinegirl
Messages
221
Reaction score
0
A rod of length 57.0 cm and mass 1.90 kg is suspended by two strings which are 41.0 cm long, one at each end of the rod. The string on side B is cut. Find the magnitude of the initial acceleration of end B.

I tried using torque= I* alpha
torque= L x f= (.57)(18.62)=10.6
I got from Newton's 2nd law, (9.8)(1.90)
so, 10.6 = I* alpha
I= (1/12)(mL^2)= (1/12)(1.90 * (.57)^2= .051
so, 10.6 = .051 alpha
alpha = 207.8 rad/s^2
alpha= a/L
207.8 = a / .57
a= 118.4 m/s ^2

This isn't right... can someone please help me?
 
Physics news on Phys.org
First, the place that it is rotating around is at one end of the rod.
How far from this is the rod's center-of-mass?

Second,
Newton's 2nd law is "Sum of Forces = ma"
Maybe you mean Newton's 4th Law "Force by gravity = m g = m GM/r^2"
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top