Question

A 30 kg child on a 2 m long swing is released from rest when the swing supports make an angle of 34 ◦ with the vertical. The acceleration of gravity is 9.8 m/s 2 . If the speed of the child at the lowest position is 2.31547 m/s, what is the mechanical energy dissipated by the various resistive

Answer 1

The question is related to calculating the mechanical energy dissipation of a child on a swing. The initial potential energy is calculated and compared with the kinetic energy at the lowest point to determine the energy lost due to resistive forces like air resistance and friction.

Step-by-step explanation:

The student is asking about the mechanical energy dissipation of a child on a swing due to various resistive forces such as air resistance or friction at the pivot point of the swing. The scenario involves calculating the difference between the initial potential energy and the kinetic energy at the lowest point of the swing to determine the amount of energy that has been lost due to these resistive forces.

Given that the swing is 2 m long, and the child is released from an angle of 34 degrees with the vertical, one can calculate the initial height of the child and subsequently the initial potential energy using the formula for potential energy, PE = mgh, where m is mass, g is acceleration due to gravity, and h is height. The kinetic energy at the lowest point of the swing can be determined using the formula KE = 0.5mv², where m is mass and v is velocity. The mechanical energy dissipated is the difference between the initial potential energy and the kinetic energy at the lowest point.

However, the provided information indicates that the velocity (2.31547 m/s) and mass (30 kg) of the child at the lowest position do not account for all the potential energy the child had at the start, signifying energy dissipation due to resistive forces.

Answer 2

Energy dissipated = 13.453 Joules

Step-by-step explanation:

In order to solve this problem, we first compute the gravitational potential energy the child has, and then find the kinetic energy at the lowest position.

The gravitational potential energy (relative to lowest position) is found as follows:

G.P.E = mass * gravity * height

Where, Height = 2 - 2 * Cos(34°)

Height = 0.3193 meters

G.P.E = 30 * 9.8 * 0.3193

G.P.E = 93.874 J

Kinetic energy:

K.E = 0.5 * mass * velocity^2

K.E = 0.5 * 30 * 2.31547^2

K.E = 80.421 J

Energy dissipated = G.P.E - K.E

Energy dissipated = 93.874 - 80.421

Energy dissipated = 13.453 J