Calculate the torque about the front support of a diving board, exerted by a 70 kg person 3.0 m from that support. (Take the positive direction to be clockwise.)
Torque = M g L
L is the distance of diver from support
The sign depends upon which side the board is supported. You didn't say
answer
To calculate the torque exerted by a person on a diving board, we need to use the formula:
Torque = Force x Distance
First, we need to calculate the force exerted by the person. The force can be calculated using the formula:
Force = Mass x Acceleration due to gravity
Given that the mass of the person is 70 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force as follows:
Force = 70 kg x 9.8 m/s^2
Force = 686 N
Now, we can calculate the torque using the given distance from the support. The distance is given as 3.0 m.
Torque = Force x Distance
Torque = 686 N x 3.0 m
Torque = 2058 N·m
Therefore, the torque exerted by the person on the diving board about the front support is 2058 N·m (clockwise).
To calculate the torque exerted by the person on the diving board, we need to understand the concept of torque and apply the formula for torque.
Torque (τ) is the rotational equivalent of force and depends on the distance from the axis of rotation. It is given by the formula:
τ = r × F
Where:
τ = Torque (in Newton-meters or Nm)
r = Distance from the axis of rotation (in meters)
F = Applied force (in Newtons or N)
In this case, the person's weight (force) is causing the torque as they lean on the diving board. We need to consider both the magnitude of the force and the distance from the front support.
Given:
Weight of the person (force) = 70 kg
Distance from the front support (r) = 3.0 m
To calculate the force exerted by the person, we will use the formula:
Force (F) = Weight = mass × gravitational acceleration
Gravitational acceleration (g) on Earth is approximately 9.8 m/s².
Therefore, the force exerted by the person is:
F = 70 kg × 9.8 m/s²
Now, we can calculate the torque using the formula:
τ = r × F
Substituting the values:
τ = 3.0 m × (70 kg × 9.8 m/s²)
Calculating the value of the expression inside the parentheses:
τ = 3.0 m × (686 N)
Finally, we can calculate the torque:
τ = 2058 Nm
So, the torque exerted by the 70 kg person at a distance of 3.0 m from the front support of the diving board is 2058 Newton-meters (Nm), in the clockwise direction (as specified).