(I) What is the mass of the diver in Fig. 9-49 if she exerts a torque of 1800 m·N on the board,

step 1 So once again, welcome to a new problem. This time we have a diver and she is being supported by

(I) What is the mass of the diver in Fig. 9-49 if she exerts...

Key Concepts

Mass-Weight Relationship

The mass-weight relationship connects an object's mass to the gravitational force acting on it. Weight is the product of mass and the acceleration due to gravity. In torque calculations involving weights, this relationship is used to convert an object's mass into the force that produces torque about a pivot point.

Static Equilibrium

Static equilibrium refers to the condition when an object is at rest and the sum of all forces and torques acting on it is zero. This principle is essential in problems involving beams, boards, or any structures supported at multiple points, allowing the determination of unknown forces, weights, or masses by balancing moments and forces.

Lever Arm

The lever arm is the distance from the pivot point at which a given force is applied. It defines how effective a force is at producing rotation. A larger lever arm means the same amount of force can generate a larger torque, making this concept fundamental when analyzing rotational systems and moments.

Torque

Torque, also known as the moment of force, is a measure of the tendency of a force to rotate an object about a pivot or axis. It is calculated as the product of the force and the perpendicular distance from the pivot point (the lever arm) to the line of action of the force. In problems of rotational mechanics, understanding torque is crucial to relating applied forces to rotational effects.

Transcript

00:01 So once again, welcome to a new problem.

00:04 This time we have a diver and she is being supported by a diving board.

00:16 So, you know, there's a diver right here and this is a diving board providing support to this diver.

00:31 And we do have a distance of one meter between the supports and also the distance between the second support and the diver happens to be three meters so happens to be three meters so we need to give some depth to the board itself to make sure it supports the diver adequately.

01:10 And the two supports.

01:11 The first one on the left is the a board, and then the second one is the b support.

01:21 This is the information that's given.

01:25 Another piece of information that will be given is the fact that when the diver bounces off on the on the on the board the talk to the diver is 1 ,800 newton meter and so given that information we want to find the mass m of the diver you know that's that's what we want to find out the diver is being supported by two reactions in b so the first thing we want to write out is the fact that the torque itself is equivalent to the perpendicular distance from the diver and the force that the diver is applying when the diver bounces that way.

02:32 The force they're applying is equivalent to their weight.

02:36 And then this would be their perpendicular distance, our perpendicular.

02:41 Just to expand the problem, if the diver will say jumping at an angle, say like that, you know, the board was at an angle, then the distance, the perpendicular distance, our perpendicular would change and the character would be, you know, r sign of theta.

03:04 So this r perpendicular would be r sign of theta, given that this angle is theta.

03:15 And that's just a general statement about what's going on with this type of problem.

03:22 And so talk becomes in this particular case the total distance from this edge a up until that edge, a, because we're computing the talk around a...

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