Why Is Tension T=2mg and Not T=mg at Time t=τ?

  • Thread starter Thread starter user5
  • Start date Start date
  • Tags Tags
    Tension
AI Thread Summary
The discussion centers on the tension in a massless rod attached to a mass m on a frictionless cart shaped like an equilateral triangle. At time t=τ, when the rod is parallel to the ground, the tension is determined to be T=2mg instead of T=mg due to the dynamics of the system as the mass falls. The radial force, expressed as mv^2/L, must equal the tension force, leading to the conclusion that the tension doubles as the mass accelerates. The torque generated by the gravitational force also plays a role in this analysis. Understanding these relationships is crucial for accurately calculating the tension in this system.
user5
Messages
38
Reaction score
0
A massless rod of length L attached to mass m and with axle to cart of mass M. The cart has a shape of equilateral triangle (edge L). the cart is at rest and its center of mass is above x=0 and a rod is perpendicular to the ground. the cart is free to move without friction. at time t=0 the mass m is released and starts to fall to the left. at time t=τ the rod is parallel to the ground. Why the tension from the stick at time t=τ is T=mv^2/L=2mg and not T=mv^2/L=mg?
 

Attachments

  • 2.JPG
    2.JPG
    11.5 KB · Views: 489
Last edited:
Physics news on Phys.org
What do you think?
Any relevant equations?
Any ideas of you?
 
mv^2/L is the radial force that need to be equated with the tension force...but the torque mgsin 90 = mg
 
Last edited:

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Uniform Circular Motion, Find the Tension
Replies
8
Views
3K
Time it Takes for a Transverse Pulse to Travel a Distance "L" Up a Cable Against Gravity?
Replies
13
Views
1K
Impulse and Momentum: Ball and cart connected by a cord
Replies
24
Views
3K
Find acceleration of a pulley system
Replies
6
Views
9K
This 3 mass atwood problem is confusing me
Replies
4
Views
952
Misunderstanding Work-energy theorem and center of mass properties
Replies
7
Views
2K
Work done on a conical pendulum
Replies
3
Views
2K
Rotating and translating spool across a table
Replies
2
Views
3K
Tension and speed of bowling ball pendulum passing the equilibrium position
Replies
2
Views
1K
Rod colliding with the ground (Special relativity question)
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top