A uniform plank of length 5.3 m and weight 228 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 446 N walk on the overhanging part of the plank before it just begins to tip?

Question

A uniform plank of length 5.3 m and weight 228 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 446 N walk on the overhanging part of the plank before it just begins to tip?

Answer 1

Set the moment about the right support equal to zero and assume that no force is exrted by the left support. (That will be the tipping condition). The weight of the plank acts through the center of mass, 1.55 m left of the right support. Thus,

228 * 1.55 = 446 * x

Solve for x.

Answer 2

To determine the distance "x" that a person can walk on the overhanging part of the plank before it just begins to tip, we need to consider the balance of moments about the supports.

Let's denote the weight of the plank as "W_plank" and the weight of the person as "W_person." Given that the weight of the plank is 228 N and the weight of the person is 446 N, we have:

W_plank = 228 N
W_person = 446 N

Now, let's calculate the distance x using the equation for the balance of moments:

For the plank not to start tipping, the sum of the clockwise moments about the left support must be equal to the sum of the counterclockwise moments about the right support.

Clockwise moments:
The weight of the plank creates a clockwise moment since it acts downward at the center of gravity, which is at a distance of (5.3 m + 1.1 m)/2 = 3.2 m from the left support. So, the moment created by the weight of the plank is:
Moment_plank = W_plank * distance from the left support = 228 N * 3.2 m

Counterclockwise moments:
The weight of the person creates a counterclockwise moment since it acts downward at the end of the overhanging part of the plank, which is at a distance of x from the right support. So, the moment created by the weight of the person is:
Moment_person = W_person * distance from the right support = 446 N * x

For equilibrium (no tipping), the clockwise moment must be equal to the counterclockwise moment:

Moment_plank = Moment_person
228 N * 3.2 m = 446 N * x

To find x, we rearrange the equation:

x = (228 N * 3.2 m) / 446 N

Now, we can plug in the values and evaluate x:

x = (228 N * 3.2 m) / 446 N
x ≈ 1.63 m

Therefore, a person can walk approximately 1.63 meters on the overhanging part of the plank before it just begins to tip.

A uniform plank of length 5.3 m and weight 228 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 446 N walk on the overhanging part of the plank before it just begins to tip?

Set the moment about the right support equal to zero and assume that no force is exrted by the left support. (That will be the tipping condition). The weight of the plank acts through the center of mass, 1.55 m left of the right support. Thus,

1.0008

To determine the distance "x" that a person can walk on the overhanging part of the plank before it just begins to tip, we need to consider the balance of moments about the supports.