Newton's second law allows to find the answers to the questions about the motion of the system are:
a) in the attachment we see the free body diagram.
b) The acceleration of the system is a= 7.3 m/s², with body 1 descending.
c) The tension in the string is T = 103.4 N
Newton's second law states that the net force on a body is equal to the product of the mass times the acceleration.
∑ F =m a
where F is the force, m the mass and a the acceleration of the body.
a) A free body diagram is a diagram of the forces without the details of the bodies, in the attachment we have a diagram of the system, two directions are indicated for the positive direction, the x axis is parallel to the inclined plane and the y axis is perpendicular to the plane.
Let's use trigonometry to find the components of the weights.
body 1
sin 60 = [tex]\frac{W_{1x}}{W_1} [/tex]
cos 60 = [tex]\frac{W_{1y}}{W_1} [/tex]
W₁ₓ = W₁ sin 60
[tex]W_{1y}[/tex] = W₁ cos 60
body 2
sin 30 = [tex]\frac{W_{2x}}{W_2} [/tex]
cos 30 = [tex]\frac{W_{2y}}{W_2} [/tex]
W₂ₓ= W2 sin 30
[tex]W_{2y}[/tex] = W2 cos 30
Let's write Newton's equations for each body and axis.
body 1
x-axis.
W₁ₓ -T = m₁ a
y-axis
N₁ – [tex]W_{1y}[/tex] =0
body 2
x-axis
T – W₂ₓ = m₂ a
y-axis
N₂ - [tex]W_{2y}[/tex] =0
Let's substitute and write our system of equations.
m₁ g sin 60 – T = m₁ a
-m₂ g sin 30 + T = m₂ a
Let's solve.
(m₁ sin 60 - m₂ sin 30) g= ( m₁+m₂) a
[tex]a = \frac{m_1 sin 60 - m_2 sin 30 }{m_1 + m_2} \ g [/tex]
Let's calculate.
[tex]a = \frac{12 \ sin 60 - 8 \ sin 35 }{ 12 + 8 } \ 9.8[/tex]
a = 7.3 m/s²
c) we substitute in some of the equations to find the tension
T -m₂ g sin 35 = m₂ a
T = m₂ ( g sin 35 + a)
Let's calculate
T = 8 (9.8 sin 35 + 7.3)
T = 103.4N
In conclusion using Newton's second law we can find the answers to the questions about the motion of the system are:
a) in the attachment we see the free body diagram.
b) The acceleration of the system is a= 7.3 m/s², with body 1 descending.
c) The tension in the string is T = 103.4 N
Learn more about Newton's second law here: brainly.com/question/25545050
