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Use the worked example above to help you solve this problem. Suppose a block with mass 2.90 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.430, what maximum angle can the ramp make with the horizontal before the block starts to slip down?

Use the worked example above to help you solve this problem. Suppose a block with mass 2.90 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.430, what maximum angle can the ramp make with the horizontal before the block starts to slip down?

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SOLUTION Write Newton's laws for a static system in component form. The gravity force has two components. Rearrange Equation (2) to get an expression for the normal force ». Substitute the expression for into Equation (1) and solve for tan 8. (1) EF-mg sin 8-p=0 (2) EP,-n-mg cos 8 = 0 n = mg cos 8 EP,-mg sin 8-pmgcos 6-0 tan 8-p tan 8=0.350-6-tan¹ (0.350) 19.3° Apply the inverse tangent function to get the answer. LEARN MORE Remarks It's interesting that the final result depends only on the coefficient of static friction. Notice also how similar Equations (1) and (2) are to the equations developed in previous problems. Recognizing such patterns is key to solving problems successfully. Question A larger static friction constant would result in a: (Select all that apply.) smaller component of gravitational force along the ramp at the maximum angle. smaller maximum angle.. larger maximum angle. Olarger component of gravitational force along the ramp at the maximum angle. Olarger component of normal face at the maximum angle. PRACTICE IT Use the worked example above to help you solve this problem. Suppose a block with mass 2.90 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.430, what maximum angle can the ramp make with the horizontal before the block starts to slip down? EXERCISE HINTS: GETTING STARTED IIM STUCK! Use the values from PRACTICE IT to help you work this exercise. The ramp in the figure is roughed up and the experiment repeated. (a) What is the new coefficient of static friction if the maximum angle turns out to be 38.902 (b) Find the maximum static friction force that acts on the block
Transcribed Image Text:SOLUTION Write Newton's laws for a static system in component form. The gravity force has two components. Rearrange Equation (2) to get an expression for the normal force ». Substitute the expression for into Equation (1) and solve for tan 8. (1) EF-mg sin 8-p=0 (2) EP,-n-mg cos 8 = 0 n = mg cos 8 EP,-mg sin 8-pmgcos 6-0 tan 8-p tan 8=0.350-6-tan¹ (0.350) 19.3° Apply the inverse tangent function to get the answer. LEARN MORE Remarks It's interesting that the final result depends only on the coefficient of static friction. Notice also how similar Equations (1) and (2) are to the equations developed in previous problems. Recognizing such patterns is key to solving problems successfully. Question A larger static friction constant would result in a: (Select all that apply.) smaller component of gravitational force along the ramp at the maximum angle. smaller maximum angle.. larger maximum angle. Olarger component of gravitational force along the ramp at the maximum angle. Olarger component of normal face at the maximum angle. PRACTICE IT Use the worked example above to help you solve this problem. Suppose a block with mass 2.90 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.430, what maximum angle can the ramp make with the horizontal before the block starts to slip down? EXERCISE HINTS: GETTING STARTED IIM STUCK! Use the values from PRACTICE IT to help you work this exercise. The ramp in the figure is roughed up and the experiment repeated. (a) What is the new coefficient of static friction if the maximum angle turns out to be 38.902 (b) Find the maximum static friction force that acts on the block
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