Use the worked example above to help you solve this problem. Suppose a block with mass 2.00 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.320, what maximum angle can the ramp make with the horizontal before the block starts to slip down? 17.7 EXERCISE HINTS: 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 and the experiment repeated. (a).What.is.the.new coefficient of static friction if the maximum angle turns out to be 29.6°? Enter a number. (b) Find the magnitude of the maximum static friction force that acts on the block. N

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PRACTICE IT
Use the worked example above to help you solve this problem. Suppose a block with mass 2.00 kg is
resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.320, what
maximum angle can the ramp make with the horizontal before the block starts to slip down?
17.7
EXERCISE
HINTS: 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 and
the experiment repeated.
(a).What.is.the.new coefficient of static friction if the maximum angle turns out to be 29.6°?
Enter a number.
(b) Find the magnitude of the maximum static friction force that acts on the block.
N
Transcribed Image Text:PRACTICE IT Use the worked example above to help you solve this problem. Suppose a block with mass 2.00 kg is resting on a ramp. If the coefficient of static friction between the block and the ramp is 0.320, what maximum angle can the ramp make with the horizontal before the block starts to slip down? 17.7 EXERCISE HINTS: 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 and the experiment repeated. (a).What.is.the.new coefficient of static friction if the maximum angle turns out to be 29.6°? Enter a number. (b) Find the magnitude of the maximum static friction force that acts on the block. N
GOAL Apply the concept of static friction to an object resting on an
incline.
PROBLEM Suppose a block with a mass of 2.50 kg is resting on a
ramp. If the coefficient of static friction between the block and ramp is
ng sin e
0.350, what maximum angle can the ramp make with the horizontal
mg cos e e
before the block starts to slip down?
STRATEGY This is an application of Newton's second law involving
an object in equilibrium. Choose tilted coordinates, as in the figure. Use the fact that the block is just
about to slip when the force of static friction takes its maximum value, f. = 4n.
SOLUTION
Write Newton's laws for a static system
(1) EF = mg sin e - u̟n = 0
in component form. The gravity force
(2) EF = n - mg cos e = 0
has two components.
Rearrange Equation (2) to get an
n = mg cos 8
expression for the normal force n.
Substitute the expression for n into
EF, = mg sin 8 - H mgcos 0 = 0 → tan 8 =u.
Equation (1) and solve for tan 0.
Apply the inverse tangent function to
get the answer.
tan e = 0.350 → 0 = tan (0.350) = 19.3°
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.)
larger component of gravitational force along the ramp at the 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.
O larger maximum angle.
Transcribed Image Text:GOAL Apply the concept of static friction to an object resting on an incline. PROBLEM Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is ng sin e 0.350, what maximum angle can the ramp make with the horizontal mg cos e e before the block starts to slip down? STRATEGY This is an application of Newton's second law involving an object in equilibrium. Choose tilted coordinates, as in the figure. Use the fact that the block is just about to slip when the force of static friction takes its maximum value, f. = 4n. SOLUTION Write Newton's laws for a static system (1) EF = mg sin e - u̟n = 0 in component form. The gravity force (2) EF = n - mg cos e = 0 has two components. Rearrange Equation (2) to get an n = mg cos 8 expression for the normal force n. Substitute the expression for n into EF, = mg sin 8 - H mgcos 0 = 0 → tan 8 =u. Equation (1) and solve for tan 0. Apply the inverse tangent function to get the answer. tan e = 0.350 → 0 = tan (0.350) = 19.3° 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.) larger component of gravitational force along the ramp at the 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. O larger maximum angle.
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