A 750-N physics student carries a 4.0 meter board, uniform in shape, and 190 newtons in weight to our swimming pool. The student then places the board on the deck and next to the pool in such a way so 1.5 meters of the board extends out over the edge of the pool. How far, in meters, may the student walk out onto the board, with tipping?
the cb of the board, from the end, is 2 m, or .5 m inland.
Sum moments about the edge of the pool.
.5*190-d*750=0 for stability
solve for d, the distance she can walk out from the edge.
Think out the equation I wrote.
To find how far the student may walk out onto the board without tipping, we need to determine the balance point or the center of mass of the board.
The balance point of the board can be calculated using the concept of torque. Torque is a measure of a force's tendency to rotate an object around a particular point. When the board is balanced, the torques on both sides of the balance point will be equal.
In this case, the torque due to the weight of the board needs to be balanced by the torque due to the weight of the student. The torque due to the weight of the board can be calculated by multiplying its weight by the distance from the balance point.
The torque due to the weight of the student can be calculated by multiplying the student's weight by the distance they walk out onto the board.
Since the board is uniform in shape, the center of mass is located at the midpoint of the board. Therefore, the balance point is at the midpoint, which is half the length of the board.
Let's calculate the balance point and the distance the student may walk out onto the board:
Length of the board = 4.0 meters
Balance point = (1/2) * Length of the board = (1/2) * 4.0 = 2.0 meters
Now, let's calculate the torques:
Torque due to the weight of the board = Weight of the board * Distance from balance point
Torque due to the weight of the student = Weight of the student * Distance walked out onto the board
Given:
Weight of the board = 190 N
Weight of the student = 750 N
Distance from balance point = 1.5 meters (the distance the board extends out)
Torque due to the weight of the board = 190 N * 1.5 m = 285 N·m
Now, we can solve for the distance the student may walk out:
285 N·m = 750 N * Distance walked out
Distance walked out = 285 N·m / 750 N
Distance walked out = 0.38 meters
Therefore, the student may walk out approximately 0.38 meters onto the board without tipping.