a 500-n diver stands at the end of 4.0-m diving board. the board is attached by two supports 1.5-m apart as shown below. find the tension in each of the of the two supports if the diving board weighs 150-n
How you compute? What is the formula ?
To find the tension in each of the two supports, we need to consider the forces acting on the diving board.
First, let's identify the forces present:
1. Weight of the diving board (150 N): This force acts vertically downwards at the center of gravity of the board.
2. Weight of the diver (500 N): This force acts vertically downwards at the position of the diver.
3. Tension force in each of the supports: These forces act at the points where the diving board is attached to the two supports. We'll call these forces T1 and T2.
To solve this problem, we will use the principle of equilibrium, which states that the net force and net torque acting on the diving board must be zero.
Since the diving board is in vertical equilibrium, the sum of the vertical forces must be zero:
ΣF y = 0
ΣF y = -150 N (weight of the diving board) - 500 N (weight of the diver) + T1 + T2 = 0
Now, let's consider the torque equilibrium. The pivot point chosen will be one of the supports. The torque of a force is given by the force multiplied by its perpendicular distance from the pivot.
Στ = 0
Στ = (-150 N) × 2.0 m (distance from the pivot) + (-500 N) × 1.5 m + T2 × 1.5 m = 0
Simplifying the above equations, we have:
-300 N + T1 + T2 = 0 ---(1)
-750 N + 1.5 T2 = 0 ---(2)
Solving these two equations simultaneously will give us the values of T1 and T2.
From equation (2), we can rearrange it to solve for T2:
T2 = (750 N) / 1.5 = 500 N
Now, substitute this value of T2 back into equation (1):
-300 N + T1 + 500 N = 0
T1 = -200 N
Since tension forces cannot be negative, we ignore the negative sign. Therefore, the tensions in the supports are as follows:
T1 = 200 N
T2 = 500 N
So, the tension in each of the two supports is 200 N and 500 N, respectively.
Try to analyze first before you solve
t1 = 883.33N
t2 = 1533.3N