Final answer:
The maximum mass that can be placed at the right end of an 86 kg, 6.0 m long uniform plank before it tips is 43 kg. This is found by equating the moments created by the mass of the plank and the additional mass at the tipping point.
Step-by-step explanation:
Calculating the Mass that Can Be Placed at the End of a Plank Before Tipping
When a uniform plank is on the verge of tipping at one end, the rotational equilibrium about the tipping point (the edge that becomes a momentary axis of rotation) must be considered.
The condition for the plank to just start tipping is that the clockwise moment due to the weight of the added mass at the right end is equal to the counterclockwise moment due to the weight of the plank acting at its center of gravity (the midpoint of the plank).
Let's denote the added mass as 'm'.
The mass of the plank is given as 86 kg, and its length is 6.0 m.
The distance from the center of the plank (center of gravity) to the tipping point is half the length of the plank, which is 3.0 m. Thus, the counterclockwise moment is the product of the plank's weight and this distance, which is (86 kg)(9.8 m/s^2)(3.0 m).
For the plank to tip, the clockwise moment due to the added mass at the right end must be equal to this. Therefore, we can set up the equation:
(m)(9.8 m/s^2)(6.0 m) = (86 kg)(9.8 m/s^2)(3.0 m)
Now, we can solve for 'm':
m = (86 kg)(3.0 m) / (6.0 m)
m = 43 kg
The maximum mass that can be placed at the right end of the plank before it tips is 43 kg.