Equilibrium Problem: Max Mass for Throckmorton on 6.0m Plank

In summary, a uniform wooden plank with a length of 6.0m and a mass of 90kg is placed on two sawhorses separated by 1.5m. The cousin, Throckmorton, tries to stand on the right-hand end of the plank. To keep the plank at rest, the cousin's weight cannot exceed the center of gravity, which is located at half of the plank's length. There is no need to find the center of gravity for the system.
  • #1
jghlee
16
0

Homework Statement



A uniform wooden plank of length L = 6.0m and mass M = 90kg rests on top of two sawhorses separated by D = 1.5m, located equal distances from the center of the plank. Your cousin Throckmorton tries to stand on the right-hand end of the plank. If the plank is to remain at rest, how massive can Throckmorton be?

The Attempt at a Solution


How do I know the Xcg value for this problem since there are two sawhorses supporting this plank?
 
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  • #2
Uniform means that the centre of gravity is at the geometrical centre of the plank. In this case, half of it's length.
 
  • #3
rock.freak667 said:
Uniform means that the centre of gravity is at the geometrical centre of the plank. In this case, half of it's length.

So even if there's a weight at the end of the plank, the center of gravity will still be at (L/2)?
 
  • #4
jghlee said:
So even if there's a weight at the end of the plank, the center of gravity will still be at (L/2)?
the cg of the plank is at L/2. The cg of the system (plank and cousin) changes, but you don't need to find it.
 

What is an equilibrium problem?

An equilibrium problem is a physics problem that involves finding the state of balance or stability in a system, where the net forces and torques acting on the system equal to zero.

What is the "Max Mass for Throckmorton" in this problem?

The "Max Mass for Throckmorton" refers to the maximum weight that can be placed on one end of a 6.0m plank without causing it to tip or rotate.

How is equilibrium determined in this problem?

In this problem, equilibrium is determined by setting the sum of the forces and torques acting on the plank equal to zero. This means that the weight of Throckmorton and any other objects on the plank must be balanced by an equal and opposite force or torque.

Why is the length of the plank important in this problem?

The length of the plank is important because it affects the lever arm and the distribution of weight on the plank. A longer plank will have a larger lever arm, meaning that a smaller force can balance a larger weight at the other end.

What factors can affect the maximum mass for Throckmorton on the plank?

The maximum mass for Throckmorton on the plank is affected by the weight of Throckmorton, the length and width of the plank, and the location of the fulcrum or pivot point. Other factors such as friction, air resistance, and the strength of the plank can also play a role.

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