an object weighs 3 lb. at 10 earth radii from its center. What is the object's weight on the earth's surface?
weight = k /r^2
weight at 10 radii = 1/100 weight at one radius
so
300 pounds
got it. thanks
To calculate the object's weight on the Earth's surface, we need to use Newton's law of universal gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Given that the object weighs 3 lb. at a distance of 10 Earth radii from its center, we can find the weight of the object on the Earth's surface, which is approximately at a distance of 1 Earth radius from its center.
Let's start by determining the gravitational acceleration at a distance of 10 Earth radii from the Earth's center.
Step 1: Calculate the gravitational acceleration at that distance.
The formula for gravitational acceleration (g) is given by:
g = G * (M / r^2)
where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the object and the Earth's center.
The gravitational constant, G, is approximately 6.674 × 10^-11 N·(m/kg)^2.
The mass of the Earth, M, is approximately 5.972 × 10^24 kg.
The distance, r, is equal to 10 times the Earth's radius, which is approximately 6.371 × 10^6 meters.
Plugging these values into the formula, we can calculate the gravitational acceleration at a distance of 10 Earth radii from the Earth's center.
g = (6.674 × 10^-11 N·(m/kg)^2) * (5.972 × 10^24 kg) / (10 * (6.371 × 10^6 meters))^2
Calculating this yields:
g ≈ 0.0663 m/s² (rounded to four decimal places)
Step 2: Calculate the weight on the Earth's surface.
The weight of an object is given by the formula:
Weight = mass * acceleration due to gravity
Since the weight is already provided as 3 lb., we need to convert it to kilograms before calculating its mass. One pound is approximately equal to 0.4536 kg.
So, 3 lb. ≈ 3 lb. * (0.4536 kg/lb.) ≈ 1.3618 kg.
Now, we can calculate the weight on the Earth's surface using the formula:
Weight = mass * acceleration due to gravity
Weight = 1.3618 kg * (9.807 m/s²)
Calculating this gives us:
Weight ≈ 13.3728 N
Therefore, the object weighs approximately 13.3728 Newtons on the Earth's surface.