A child sits down on one end of a horizontal seesaw of negligible weight, 1.96 m from the pivot point. No one balances on the other side. Find the instantaneous angular acceleration of the see-saw and the tangential linear acceleration of the child.
wonder if the entire seesaw had any weight, other than no weight on that one end.
If the mass of the child is the only mass in motion, moment of Inertia= mass*1.96^2
torque=I*angular accleration
torque= mass*g*1.96
acceleration= torque/momentofInertion= 9.8/1.96 radians/sec^2
To find the instantaneous angular acceleration of the seesaw, we can use the formula:
angular acceleration = tangential linear acceleration / radius,
where the radius is the distance from the pivot point to the child.
Given that the child is sitting 1.96 m from the pivot point, we can substitute this value into the formula. However, we don't have the tangential linear acceleration yet.
To find the tangential linear acceleration of the child, we can use the equation:
tangential linear acceleration = radius * angular acceleration.
Since we need both the angular acceleration and the radius to calculate the tangential linear acceleration, we have to use the first equation to find the angular acceleration before plugging it into the second equation.
Now, let's find the angular acceleration.
Given:
Radius (r) = 1.96 m
Since no one is balancing on the other side, the seesaw is unbalanced, and it will start rotating due to the weight of the child.
The weight of the child creates a torque that causes the rotation. The torque can be calculated using the formula:
torque = force * distance,
where the force is the weight of the child and the distance is the radius.
The weight of the child can be calculated using the formula:
weight = mass * acceleration due to gravity,
where the acceleration due to gravity is approximately 9.8 m/s².
To calculate the torque, we need to know the mass of the child.
Once we have the torque, we can use the formula:
torque = moment of inertia * angular acceleration,
where the moment of inertia depends on the shape of the seesaw. Without information about the shape, we cannot determine the exact moment of inertia.
However, if we assume that the seesaw is a thin rod pivoted at one end (about its center of mass), the moment of inertia (I) can be approximated using the formula:
moment of inertia (thin rod) = (1/3) * mass * length²,
where the length is twice the radius.
So, to find the moment of inertia, we still need to know the mass of the child.
Once you have the mass and the torque, you can calculate the angular acceleration using the formula:
angular acceleration = torque / moment of inertia.
Finally, with the angular acceleration, you can find the tangential linear acceleration using the formula:
tangential linear acceleration = radius * angular acceleration.
Note that this explanation assumes several assumptions and approximations, such as the shape and distribution of mass of the seesaw and a neglectable weight. The actual values may differ depending on these factors.