A Block on a RampGOAL Apply the concept of static friction to an object resting on anincline.EXAMPLE 4.12PROBLEM Suppose a block with a mass of 2.50 kg is resting on aramp. If the coefficient of static friction between the block and ramp is0.350, what maximum angle can the ramp make with the horizontalbefore the block starts to slip down?SOLUTIONWrite Newton's laws for a static systemin component form. The gravity forcehas two components.Rearrange Equation (2) to get anexpression for the normal force n.Substitute the expression for ŉ intoEquation (1) and solve for tan 0.STRATEGY This is an application of Newton's second law involving anobject in equilibrium. Choose tilted coordinates, as in the figure. Use the fact that the block is just aboutto slip when the force of static friction takes its maximum value, fs = μgn.Apply the inverse tangent function toget the answer.(1) ΣFx(2) ΣF,ΣF,= mg sin 0 - μ¸n = 0= n -n = mg cos 0= mg sin 0mg cosemg cos 0 = 0μmg cos 0 =tan 00.350 → 0=gmgtan-¹ (0.350)sin 800 → tan 0 =μsS= 19.3° REMARKS It's interesting that the final result depends only on the coefficient of static friction. Noticealso how similar Equations (1) and (2) are to the equations developed in previous problems. Recognizingsuch patterns is key to solving problems successfully.QUESTION A larger static friction constant would result in a: (Select all that apply.)larger maximum angle.smaller component of gravitational force along the ramp at the maximum angle.larger component of normal force at the maximum angle.smaller maximum angle.larger component of gravitational force along the ramp at the maximum angle.00330PRACTICE ITUse the worked example above to help you solve this problem. Suppose a block with mass 2.80 kg isresting on a ramp. If the coefficient of static friction between the block and the ramp is 0.400, whatmaximum angle can the ramp make with the horizontal before the block starts to slip down?23.75XYour response is within 10% of the correct value. This may be due to roundoff error, or you could have amistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimizeroundoff error.ºEXERCISEHINTS: GETTING STARTED I I'M STUCK!Use the values from PRACTICE IT to help you work this exercise. The ramp in the figure is roughed up andthe experiment repeated.(a) What is the new coefficient of static friction if the maximum angle turns out to be 36.4°?(b) Find the magnitude of the maximum static friction force that acts on the block.N

Practice: Apply the equilibrium condition of the force along the y-axis. ∑Fy=0n−mgcosθ=0n=mgcosθ

PRACTICE IT Use the worked example above to help you solve this problem. Suppose a block with mass 2.80 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.400, what maximum angle can the ramp make with the horizontal before the block starts to slip down? 23.75 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. EXERCISE HINTS: GETTING STARTED I'M 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 36.4°? (b) Find the magnitude of the maximum static friction force that acts on the block. N

PRACTICE IT Use the worked example above to help you solve this problem. Suppose a block with mass 2.80 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.400, what maximum angle can the ramp make with the horizontal before the block starts to slip down? 23.75 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. EXERCISE HINTS: GETTING STARTED I'M 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 36.4°? (b) Find the magnitude of the maximum static friction force that acts on the block. N

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

Problem 5P

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