Question

soccer is also called association football" A soccer ball is a sphere, with circumference of 70 centimeters. in developing a new material to use for a soccer ball when NASA attempts to colonize mars, you test a materials with a specific gravity of 1.21. Assume the ball will be a solid sphere made from this material. What is the weight in units of newtons [N] of the ball on Mars? Recall gravity on Mars is 3.7 meters per second squared [m/s] Recall the circumference of a circle is equal to the diameter times pi: C = πD.

Answer 1

Answer: Weight on Mars = 0.02593N

Explanation:

Given; Circumference C of Sphere = 70cm = 0.7m,

Specific Gravity S. G. of material = 1.21,

acceleration due to gravity in the Mars gm = 3.7m/s^2

We know that Weight W = mass m × acceleration due to gravity.

Let the Weight in on the Mars be Wm.

Wm = m × gm

Since we are given gm, we need to calculate for m. (Note that mass m is the same everywhere)

But mass = specific gravity × volume

Since we know the specific gravity, let's go ahead to calculate for the volume of the ball.

We know that Volume of a Sphere V = (4/3)πr^3

To get r, we know that C = 2πr

Therefore, r = C/(2π) = 0.7/(2π) = (7/10)/2π = 7/20π (in meters)

V = (4/3)*π×(7/20π)^3 = 343/6000π^2 (in meter^3)

m = 343/6000π^2 × 1.21 = 7.01×10^(-3)kg

Wm = 7.01×10^(-3) × 3.7 = 0.02593N