Question

The formulae to find the mechanical energy are:

P. E = mgh and K. E = ½mv².
a. What is the common factor that affects both forms of energy?
b. How does height affect the potential energy of a body?
c. Kinetic energy of a person who is running will be more than a person who is walking. Justify.
A. a. Mass; b. It increases potential energy; c. True
B. a. Velocity; b. It decreases potential energy; c. False
C. a. Height; b. It doesn't affect potential energy; c. True
D. a. Gravitational constant; b. It decreases kinetic energy; c. False

Answer 1

Gravity affects both potential and kinetic energy, and potential energy increases with height due to its direct proportionality to height in the formula PE = mgh. Kinetic energy is greater for a running person than a walking person due to the velocity factor in the formula KE = ½mv². The conservation of mechanical energy allows for the conversion between gravitational potential and kinetic energy.

Step-by-step explanation:

When objects move or are positioned within a gravitational field, they possess two main forms of energy: potential energy (PE) and kinetic energy (KE). The two formulae for finding mechanical energy, which considers both PE and KE, are PE = mgh and KE = ½mv², where m is mass, g is the acceleration due to gravity, h is height, and v is velocity.

Gravity is a common factor that affects both forms of energy. Potential energy increases as the height of an object in a gravitational field increases. This is because PE is directly proportional to height as shown by the formula PE = mgh.

The kinetic energy of a running person is more than a walking person due to the velocity portion of the formula

KE = ½mv². More velocity results in higher kinetic energy.

Gravitational potential energy may convert to kinetic energy, and vice versa, while the total mechanical energy remains constant in an isolated system—a concept known as the Law of Conservation of Mechanical Energy.