Two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. The block in (Figure 1) has a mass m = 10 kg and is being pulled by a force F on a table with coefficient of static friction μg = 0.3. Four forces act on it: • The applied force F (directed 0 = 30° above the horizontal). • The force of gravity F, = mg (directly down, where g = 9.8 m/s²). The normal force N (directly up). • • The force of static friction f (directly left, opposing any potential motion). If we want to find the size of the force necessary to just barely overcome static friction (in which case f = μN), we use the condition that the sum of the forces in both directions must be 0. Using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: F cos 0-μ, N=0 • Fsin 0+N-mg=0 In order to find the magnitude of force F, we have to solve a system of two equations with both F and the normal force N unknown. Use the methods we have learned to find an expression for F in terms of m, g. 8, and μg (no N). Express your answer in terms of m, g, 0, and μg.

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Part F - Example: Finding Two Forces (Part I)
Two dimensional dynamics often involves solving for two unknown quantities in two
separate equations describing the total force. The block in (Figure 1) has a mass
m = 10 kg and is being pulled by a force F on a table with coefficient of static
friction μ = 0.3. Four forces act on it:
• The applied force F (directed 0 = 30° above the horizontal).
• The force of gravity F = mg (directly down, where g = 9.8 m/s²).
• The normal force N (directly up).
• The force of static friction f (directly left, opposing any potential
motion).
If we want to find the size of the force necessary to just barely overcome static
friction (in which case fs = μg N), we use the condition that the sum of the forces
in both directions must be 0. Using some basic trigonometry, we can write this
condition out for the forces in both the horizontal and vertical directions,
respectively, as:
• F cos 0 - μg N=0
• Fsin 0+N-mg=0
In order to find the magnitude of force F, we have to solve a system of two
equations with both F and the normal force N unknown. Use the methods we
have learned to find an expression for F in terms of m, g, 0, and μg (no N).
Express your answer in terms of m, g, 0, and μg.
Transcribed Image Text:Part F - Example: Finding Two Forces (Part I) Two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. The block in (Figure 1) has a mass m = 10 kg and is being pulled by a force F on a table with coefficient of static friction μ = 0.3. Four forces act on it: • The applied force F (directed 0 = 30° above the horizontal). • The force of gravity F = mg (directly down, where g = 9.8 m/s²). • The normal force N (directly up). • The force of static friction f (directly left, opposing any potential motion). If we want to find the size of the force necessary to just barely overcome static friction (in which case fs = μg N), we use the condition that the sum of the forces in both directions must be 0. Using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: • F cos 0 - μg N=0 • Fsin 0+N-mg=0 In order to find the magnitude of force F, we have to solve a system of two equations with both F and the normal force N unknown. Use the methods we have learned to find an expression for F in terms of m, g, 0, and μg (no N). Express your answer in terms of m, g, 0, and μg.
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