Determine the net force (Fnet) on an object that experiences the forces shown. SP2. Obtain, evaluate, and communicate information about how forces affect the motion of objects..c.

Use mathematical representations to calculate magnitudes and vector components for typical forces

including gravitational force, normal force, friction forces, tension forces, and spring forces

20 N of downward gravity force

15 N of rightward applied force

20 N of upward normal force

10 N of leftward friction force

a) F_{net } = 5 i ^ N ,   b) F_{net } = 5 N,  θ = 0

Explanation:

Force is a vector magnitude, one of the easiest methods to work with it is to use its Cartesian components and perform the sum on each axis in scalar form.

Therefore we will create a coordinate system and sum on each axis

X axis

          = F₁ + F₂

where they indicate the value of each one

F₁ = 15 N i ^

F₂ = -10 N i ^

where on the x-axis the direction to the right is positive

           F_{net x} = 15 - 10

           F_{net x} = 5 N

Y Axis

          F_{net y}  = F₃ + F₄

the values of this force are given and the upward direction is taken as positive

   F₃ = 20 N j ^

   F₄ = -20 N j ^

we calculate

           F_{net y} = 20 -20

           F_{net x} = 0

we can give the result in two ways

a) F_{net } = 5 i ^ N

b) in the form of module and angle.

Let's use the Pythagorean theorem

        F_{net }² = F_{net x}² + F_{net y}²

        F_{net }² = 5² + 0²

        F_{net } = 5 N

we use trigonometry for the angles

        tan θ = F_{net yy} / F_{net y}

        θ = tan⁻¹ (0/5)

         θ = 0

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2