Question

You are standing on the surface of a planet that has spherical

symmetry and a radius of 5.00 x 10⁶ m. The gravitational potential energy
U of the system composed of you and the planet is -1.20 * 10⁺⁹ J
if we choose U to be zero when you are very far from the planet. What
is the magnitude of the gravity force that the planet exerts on you when
you are standing on its surface?

Answer 1

The planet exerts a gravitational force of 240 Newtons on a person standing on its surface, calculated using the gravitational potential energy and the planet's radius.

Step-by-step explanation:

To calculate the magnitude of the gravity force exerted on a person standing on the surface of a planet, we can use the formula derived from the conservation of energy that equates the gravitational potential energy (U) to the person's weight multiplied by the planet's radius (W = -U / r). Since we know the gravitational potential energy (U = -1.20 * 10⁹ J) and the planet's radius (r = 5.00 * 10⁶ m), we can find the weight (W), which is the force due to gravity.

The weight W is calculated using the following steps:

• W = -U / r
• W = -(-1.20 * 10⁹ J) / (5.00 * 10⁶ m)
• W = (1.20 * 10⁹ J) / (5.00 * 10⁶ m)
• W = 240 N

Therefore, the planet exerts a gravitational force of 240 Newtons on the person.