Lesson 10/4

Lesson 10/4

Forces in 2-dimension

Open Ended

Journal - On an inclined plane, how should you draw the x-axis?

Example Problem

A kid has a mass of 45 kg and is going down a slide sloped at 27°. The coefficient of kinetic friction is 0.23. How fast does she slide 1.0 s after starting from rest?

Solving the Problem

• Establish a coordinate system

• Draw a free body diagram that shows the forces acting on the girl as she travels down the slide

• The three forces acting on the girl are the normal force, kinetic friction, and the girls weight.

Knowns

• mass = 45 kg

• 𝜇_s = 0.23

• t = 1.0 s

• 𝜙 = 27°

• v_i = 0 m/s

Unknowns

• a =

• v_f =

• 𝜭 =

• 
  

• 
  

First, lets find 𝜭

In this case, 𝜭 = 270° + 𝜙. So, 270° + 27° = 297°

Next let's work on the y-direction

• Add forces in the y-direction to find F_Nmg

• F_N + F_gy = F_net,y

• F_N = -F_gy

• F_N = -mg(sin𝜭)

Now the x-direction

• F_{net, x} = F_gx - F_f

• ma_x = mg(cos 𝜭) - 𝜇_sF_N

• ma = mg(cos 𝜭) + 𝜇_smg(sin 𝜭)

• a = g(cos 𝜭 + 𝜇_{s sin} 𝜭)

• a= 9.8 m/s²)(cos 297 + 0.23)(sin 297)

• 2.4 m/s²

Finally, the velocity

• v_f = v_{i + at}

• v_f = 0.0 m/s + (2.4 m/s²)(1.0 s)

• 2.4 m/s

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Take a deep breath!

• Try yesterday's assignment