A 5m long diving board of negligible mass is supported by two pillars. One pillar is at the end of left of the diving board, the other is 1.50m away. Find the forces exerted by the pillars when a 90kg diver stands at the far end of the board.
Response
I need a solution
To find the forces exerted by the pillars, we can use the principle of torque. Torque is the product of force and the perpendicular distance from the point of rotation. In this case, the point of rotation is the left end of the diving board.
Let's assume that the force exerted by the left pillar is F1N and the force exerted by the right pillar is F2N.
The torque exerted by the diver's weight can be given by the following equation:
Torque = force * perpendicular distance
The torque exerted by the diver's weight is equal to the torque exerted by the forces exerted by the two pillars.
Torque exerted by the diver's weight = Torque exerted by the forces exerted by the pillars
The weight of the diver can be calculated using the formula: weight = mass * acceleration due to gravity
Weight of the diver = 90 kg * 9.8 m/s^2
Now, let's calculate the torque exerted by the diver's weight:
Torque exerted by the diver's weight = weight of the diver * perpendicular distance
Torque exerted by the diver's weight = (90 kg * 9.8 m/s^2) * 5.00 m
Now, let's calculate the torque exerted by the forces exerted by the pillars:
Torque exerted by the forces exerted by the pillars = (F1N * 0 m) + (F2N * 1.50 m)
Since the diving board is in equilibrium, the torques exerted by the diver's weight and the forces exerted by the pillars must be equal:
Torque exerted by the diver's weight = Torque exerted by the forces exerted by the pillars
(90 kg * 9.8 m/s^2) * 5.00 m = (F1N * 0 m) + (F2N * 1.50 m)
Simplifying this equation, we get:
4410 N*m = 1.5 * F2N
Now, solving for F2N:
F2N = 2940 N
Therefore, the force exerted by the right pillar is 2940 N.
Since the diving board is in equilibrium, the sum of the forces exerted by the two pillars must equal the weight of the diver:
F1N + F2N = weight of the diver
F1N + 2940 N = 90 kg * 9.8 m/s^2
F1N = 882 N
Therefore, the force exerted by the left pillar is 882 N.
To find the forces exerted by the pillars, we need to consider the rotational equilibrium of the diving board.
First, let's calculate the torques acting on the diving board. Torque is defined as the product of the force acting on an object and the distance from the pivot point (in this case, the end of the diving board). The torques acting on the diving board should balance out to keep it in rotational equilibrium.
Let's assume the left side of the diving board is the pivot point. The torque exerted by the 90kg diver standing at the far end of the board can be calculated as follows:
Torque = force x distance
= (mass x acceleration due to gravity) x distance
= (90kg x 9.8m/s^2) x 5m
Now, since the diving board is in equilibrium, the total torque exerted by the diver must be balanced by the torques exerted by the pillars.
The left pillar, being the pivot point, exerts no torque.
The right pillar, situated 1.50m away from the pivot point, exerts a torque in the opposite direction to balance out the torque exerted by the diver.
So, we can set up the following equation:
Torque exerted by the diver = Torque exerted by the right pillar
(90kg x 9.8m/s^2) x 5m = Force exerted by the right pillar x 1.50m
Now, we can solve for the force exerted by the right pillar:
Force exerted by the right pillar = (90kg x 9.8m/s^2 x 5m) / 1.50m
Simplifying this equation will give us the force exerted by the right pillar.