Question

Find the maximum velocity possible for the person on the swing.

if someone could explain with work that would be very much appreciated since I wasn't there when this was discussed in class.

Answer 1

Answer:

The maximum possible speed is 4.85 m/s.

Explanation:

The Principle Of Conservation Of Mechanical Energy

In the absence of friction, the total mechanical energy is conserved. It means that :

$E_m=U+K$ is constant, being U the potential energy and K the kinetic energy

U=mgh

Where m is the mass of the object, g is the gravitational acceleration and h is the height from a fixed reference.

$\displaystyle K=\frac{mv^2}{2}$

Where v is the speed.

When the person is at a maximum height of 2 meters, the speed is 0. Thus the mechanical energy is made only of potential energy.

Let's fix the reference for the height to the point where the person is at minimum height (1 m from the ground level). The maximum height with respect to this reference is h=2.2 m - 1 m = 1.2 m.

The potential energy is:

U = m*9.8*1.2

U = 11.76m

When the person is at the minimum (zero) height, the mechanical energy is made only of kinetic energy. Since the mechanical energy is conserved, then:

$\displaystyle \frac{mv^2}{2}=11.76m$

Multiplying by 2 and simplifying by m:

$v^2=2*11.76=23.52$

Solving for v:

$v=\sqrt{23.52}=4.85$

$\boxed{v=4.85}$

The maximum possible speed is 4.85 m/s.