A horizontal 791 N merry-go-round is a solid disk of radius 1.48 m, started from rest by a constant horizontal force of 50.0 N applied tangentially to the edge of the disk. Find the kinetic energy of the disk after 3.01 s.
I am having trouble on which formula to exactly use for this problem. i no KE=.5mv^2 but how would it translate to this problem.
KineticEnergy=1/2 I* w^2
find w from
Torque=I*alpha
force*radius=I * alpha
w=alpha*time
so t clarify W can be found through alpha times time?
also, what does I stand for?
To find the kinetic energy of the disk after 3.01 seconds, you can use the formula:
Kinetic Energy (KE) = 0.5 * moment of inertia * angular velocity^2
To use this formula, you need to find the moment of inertia and the angular velocity of the disk.
The moment of inertia (I) of a solid disk rotating about its central axis is given by:
I = (1/2) * mass * radius^2
In this case, the mass is not given directly, but we can use the formula:
mass = total force / acceleration
The total force acting on the disk is the tangential force applied at the edge of the disk, which is 50.0 N.
To find the acceleration, we can use Newton's second law:
mass * acceleration = total force
Rearranging the equation, we have:
acceleration = total force / mass
Now, we can find the mass:
mass = total force / acceleration
= 50.0 N / a
Substituting the values, we find:
mass = 50.0 N / a
Next, we need to calculate the acceleration. The torque applied to the disk is given by the formula:
Torque = moment of inertia * angular acceleration
Since the force applied is tangential to the edge of the disk, the torque can be calculated as:
Torque = moment of inertia * (radius * angular acceleration)
Given that the torque is equal to the total force multiplied by the radius of the disk, we can equate them:
Torque = total force * radius
Substituting the values:
moment of inertia * (radius * angular acceleration) = total force * radius
Simplifying this equation:
moment of inertia * angular acceleration = total force
We know the total force is 50.0 N, so we have:
moment of inertia * angular acceleration = 50.0 N
Now, we need to find the angular acceleration. The relation between linear acceleration and angular acceleration is given by the formula:
linear acceleration = radius * angular acceleration
Rearranging the equation, we have:
angular acceleration = linear acceleration / radius
Since the linear acceleration is equal to the total force divided by the mass, we can substitute the values:
angular acceleration = total force / (mass * radius)
Now, we have all the information we need to calculate the moment of inertia, angular acceleration, and angular velocity.
To find the kinetic energy, we can now use the formula:
KE = 0.5 * moment of inertia * angular velocity^2
Finally, plug in the values into the formula and calculate the kinetic energy.