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

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.