To determine the acceleration of the block, we'll follow these steps:
1. Identify the forces acting on the block:
- The applied force pulling the block is 200 N.
- The frictional force opposing the motion is 50 N.
2. Calculate the net force:
The net force is the difference between the applied force and the frictional force.
[tex]\[
\text{Net force} = \text{Applied force} - \text{Frictional force}
\][/tex]
Given:
[tex]\[
\text{Applied force} = 200 \, \text{N}
\][/tex]
[tex]\[
\text{Frictional force} = 50 \, \text{N}
\][/tex]
Therefore:
[tex]\[
\text{Net force} = 200 \, \text{N} - 50 \, \text{N} = 150 \, \text{N}
\][/tex]
3. Calculate the acceleration using Newton's Second Law:
Newton's Second Law states that the acceleration [tex]\(a\)[/tex] of an object is given by the net force [tex]\(F_{\text{net}}\)[/tex] acting on it divided by its mass [tex]\(m\)[/tex].
[tex]\[
a = \frac{F_{\text{net}}}{m}
\][/tex]
Given:
[tex]\[
F_{\text{net}} = 150 \, \text{N}
\][/tex]
[tex]\[
m = 50 \, \text{kg}
\][/tex]
Therefore:
[tex]\[
a = \frac{150 \, \text{N}}{50 \, \text{kg}} = 3 \, \text{m/s}^2
\][/tex]
So, the net force acting on the block is 150 N, and the acceleration of the block is [tex]\( 3 \, \text{m/s}^2 \)[/tex].
