Question

If m1 = 12 Kg, Θ1 = 60 °

Answer 1

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

Second law of Newton.

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.

Free-Body diagram.

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 = $\frac{W_{1x}}{W_1}$

         cos 60 = $\frac{W_{1y}}{W_1}$

         W₁ₓ = W₁ sin 60

         $W_{1y}$  = W₁ cos 60

body 2

        sin 30 = $\frac{W_{2x}}{W_2}$

        cos 30 = $\frac{W_{2y}}{W_2}$

        W₂ₓ= W2 sin 30

        $W_{2y}$ = 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 – $W_{1y}$  =0

body 2

x-axis

          T – W₂ₓ = m₂ a

y-axis

          N₂ - $W_{2y}$  =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

       $a = \frac{m_1 sin 60 - m_2 sin 30 }{m_1 + m_2} \ g$

Let's calculate.

       $a = \frac{12 \ sin 60 - 8 \ sin 35 }{ 12 + 8 } \ 9.8$

       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