In the diagram below, how far from the end of the board can a 60 kg person walk before it will tip over? The mass of the board is 100 kg, and a 2-meter section of its 6-meter length hangs over the edge. Assume that the entire mass of the board acts at the center of the board.
Its A. 1.33
actually -_-
this is what i have
mass of the board is 100 kg, and a 2-meter section of its 6-meter length hangs over the edge. Assume that the entire mass of the board acts at the center of the board.
A. 1.33 meters
B. 1 meter
C. 2 meters
D. 0.33 meters
E. 0.5 meters
but the answer is 1.66 hmmm :/
It must be considering that the 2m over the edge have a downward force that wishes to tip the board even though it says that the mass is in the center...
ahhhh I miss read so the answer is D .33 meters from the end of the board... I apologize
To determine how far from the end of the board a 60 kg person can walk before it tips over, we need to consider the equilibrium of torques.
A torque is a force that causes an object to rotate. It is calculated by multiplying the force applied by the distance from the pivot point (or axis of rotation).
In this case, the pivot point is at the edge of the board, and we want to find the point at which the torque on one side of the pivot is equal to the torque on the other side, ensuring equilibrium.
Let's analyze the forces acting on the board:
1. The weight of the board (F_board = mass_board * gravity)
F_board = 100 kg * 9.8 m/s^2 = 980 N
2. The weight of the person (F_person = mass_person * gravity)
F_person = 60 kg * 9.8 m/s^2 = 588 N
Since the entire mass of the board acts at the center of the board, the weight of the board can be considered as acting at its mid-point. Therefore, the distance between the pivot point and the weight is half the length of the board.
Length of the board = 6 meters
Distance between the pivot point and weight (l_board) = 6 meters / 2 = 3 meters
Now, let's calculate the torque due to the weight of the board (τ_board) and the torque due to the weight of the person (τ_person):
τ_board = F_board * l_board = 980 N * 3 m = 2940 Nm
τ_person = F_person * l_person
We want torque_board = torque_person for the system to be in equilibrium and not tip over.
τ_board = τ_person
2940 Nm = F_person * l_person
Rearranging the equation, we can solve for the distance from the pivot point:
l_person = 2940 Nm / (mass_person * gravity)
l_person = 2940 Nm / (60 kg * 9.8 m/s^2)
l_person = 4.90 m
So, the person can walk up to 4.90 meters from the end of the board before it tips over.