The mechanical advantage of the screwdriver that is being described above is equal to 75N. This means that for every 30N that is applied on the screwdriver, this simple machine would in turn apply 75N of force to the lid of the can.
Answer:
The velocity of the blades is 88.185 m/s.
Explanation:
Given;
length of the blade, r = 80 m
angular speed, ω = 1 rev per 5.7 seconds
The velocity of the blades is calculated by applying the following circular motion equation that relates linear velocity (V) and angular speed (ω);

Therefore, the velocity of the blades is 88.185 m/s.
Answer:
Explanation:
Hi!
In order to obtain the Lagrangian of the system we must first write the Kinetic and Potential Energies. Lets orient our axes such that the axis of the cone coincide with the z axis. In cilindrical coordinates we have
- (1)
But, since the particle is constrained to move on the surface of the cilinder, we have the following relation between r and z:

or:
- (2)
and:
replacing (2) in (1) we obtain:
- (3)
Now the kinetic energy is given as:
- (4)
And the potential energy is given by:

So the Langrangian is given by:

And the equations of motion are:
For θ

For r

Obtained from the Euler-Langrange equations
Here the conserved quantity is given by the first equation of motion, namely:

Which is the magnitude of the angular momentum