There are 3 forces applied to a mass of 82.9 kg. Force 1 has a magnitude of 75.7 N at an angle of 41.5 degrees above the positive x-axis. Force 2 has a magnitude of 10.9 N at an angle of 62.5 degrees above the negative x-axis. Force 3 has a magnitude of 72.1 N at an angle of 35.2 degrees below the positive x-axis. What is the magnitude of the acceleration of the mass

The magnitude of the acceleration of the mass is 1.34m/s²

Explanation:

Check attachment for diagram

According to Newton's second law,

Force = mass × acceleration

Since we have more than force experienced by the object, we will take the summation of the forces along the positive x axis i.e

ΣFx = max where

m is the mass of the object

ΣFx is the summation of the forces

ax is the magnitude of the acceleration of the mass

Given mass = 82.8kg

ΣFx = 75.7cos41.5° + (-10.9cos62.5°) + 72.1cos35.2°

ΣFx = 75.7cos41.5° - 10.9cos62.5°) + 72.1cos35.2°

ΣFx = 110.58N

From the formula

ax = ΣFx/m

ax = 110.58/82.8

ax = 1.34m/s²

area of focus

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.