-GMm/r

Definition

-GMm/r is a mathematical expression that represents the gravitational potential energy per unit mass at a distance r from a point mass M, where G is the gravitational constant. This term is crucial in understanding the concept of electric potential, as it is analogous to the potential energy per unit charge in an electric field.

5 Must Know Facts For Your Next Test

1. The negative sign in -GMm/r indicates that the gravitational potential energy is always negative, meaning it decreases as the distance from the mass increases.
2. The gravitational potential energy per unit mass, -GMm/r, is directly proportional to the mass of the object (M) and inversely proportional to the distance from the object (r).
3. The gravitational potential energy per unit mass has the same form as the electric potential energy per unit charge, which is given by the expression q*V, where q is the charge and V is the electric potential.
4. The gravitational potential energy per unit mass, -GMm/r, is a scalar quantity, meaning it has only a magnitude and no direction.
5. The concept of gravitational potential energy per unit mass is essential in understanding the motion of objects in a gravitational field, as well as the behavior of charges in an electric field.

Review Questions

• Explain the relationship between the gravitational potential energy per unit mass, -GMm/r, and the electric potential energy per unit charge, q*V.
  • The gravitational potential energy per unit mass, -GMm/r, and the electric potential energy per unit charge, q*V, have the same mathematical form, with the only difference being the physical quantities involved. Both expressions represent the potential energy per unit of the respective quantity (mass or charge) at a given distance from a source (mass or charge). This analogy between gravitational and electric potential energy is important in understanding the similarities and differences between these two fundamental physical concepts.
• Describe how the sign of the gravitational potential energy per unit mass, -GMm/r, affects its interpretation.
  • The negative sign in the expression -GMm/r indicates that the gravitational potential energy is always negative. This means that the potential energy decreases as the distance from the mass increases. The negative sign reflects the fact that the gravitational force is always attractive, pulling objects towards the mass. This is in contrast to the electric potential energy, which can be either positive or negative depending on the sign of the charge. The negative sign in the gravitational potential energy per unit mass expression is an important feature that distinguishes it from the electric potential energy per unit charge.
• Analyze the factors that influence the value of the gravitational potential energy per unit mass, -GMm/r, and explain how changes in these factors affect the potential energy.
  • The gravitational potential energy per unit mass, -GMm/r, is influenced by three key factors: the gravitational constant (G), the mass of the object (M), and the distance from the object (r). The gravitational constant (G) is a universal physical constant that does not change. However, the mass of the object (M) and the distance from the object (r) can vary. Increasing the mass (M) will result in a larger magnitude of the potential energy, while increasing the distance (r) will decrease the magnitude of the potential energy. These relationships demonstrate the inverse square dependence of the gravitational potential energy per unit mass on the distance from the object, which is a fundamental principle in understanding the behavior of objects in a gravitational field.

Related terms

Gravitational Potential: The potential energy per unit mass at a given location in a gravitational field.

Electric Potential: The potential energy per unit charge at a given location in an electric field.

Point Charge: An idealized electric charge that is concentrated at a single point in space.