A pendulum is made by letting a 4 kg mass swing at the end of a string that has a length of 1.5 meter. The maximum angle that the string makes with the vertical is 30 degrees (in both directions). What is the change in the potential energy of the mass as it moves from the lowest point to the highest point of its path?

Approximately .

Explanation:

The change in the gravitational potential energy of the pendulum is directly related to the change in its height.

Refer to the sketch attached. The pendulum is initially at . Its highest point is at . The length of segment gives the change in its height.

The lengths of and are simply the length of the string, . To find the length of , start by calculating the length of .

forms a leg in the right triangle . Besides, it is adjacent to the angle . Its length would be:

.

The length of would thus be

.

The change in gravitational potential energy can be found with the equation

. In this equation,

is the mass of the object, near the surface of the earth, and is the change in the object's height.

In this case, and . Therefore:

.

The radiation of the fire causes the saucepan to heat up. the conduction of the saucepan then to distribute the heat over the saucepan and to give heat to the water. the convection of the water distributing the heat within the water, till all the water is boiling

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