Answer :
Answer:
Torque = 1015 ft.lb
Explanation:
Torque is defined as the turning effect of force. It is the force that can cause an object to rotate and gain some angular acceleration. Torque is basically an angular analog of force. The method to calculate torque is simple. Take the perpendicular distance from the line of action of force to the axis of rotation. Multiply this distance with the magnitude of force. The magnitude of this product gives the torque. Therefore,
Torque = (Force)(Perpendicular Distance)
Since, the diver is standing at the end of diving board.
Therefore,
Perpendicular Distance = 7 ft
Force = 145 lb
Therefore,
Torque = (145 lb)(7 ft)
Torque = 1015 ft.lb
To calculate the torque, the diver's weight is converted to newtons and multiplied by the board's length in meters. The torque exerted by the diver is approximately 1374.7 N·m.
The question asked involves calculating the magnitude of torque exerted by a diver on a diving board. The formula to find torque (τ) is τ = r × F × sin(θ), where r is the distance from the pivot point to the point where the force is applied, F is the force, and θ is the angle between the force vector and the lever arm (in this case, due to gravity acting vertically, θ will be 90 degrees, making sin(θ) equal to 1).
To convert the diver’s weight from pounds to newtons, we use the conversion factor 1 lb ≈ 4.44822 N. Therefore, the diver’s weight in newtons is 145 lb × 4.44822 N/lb ≈ 645 N. The distance r will be the length of the diving board in meters: 7 ft × 0.3048 m/ft ≈ 2.1336 m. Inserting these values into the torque formula: τ = 2.1336 m × 645 N ∈ 1374.7 N·m.
This number represents the torque the diver applies at the edge of the diving board, which affects how the board is bent and ultimately contributes to the diver’s jump and angular momentum as they leave the diving board.
