Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
Approximately 31 degrees
B
Approximately 45 degrees
C
Approximately 60 degrees
D
Approximately 75 degrees
Understanding the Answer
Let's break down why this is correct
Answer
The block stays put when the static‑friction force can counter the downhill pull of gravity. The downhill pull is \(mg\sin\theta\) and the friction force is at most \(\mu_s N = \mu_s mg\cos\theta\). Setting the two equal gives \(\mu_s mg\cos\theta = mg\sin\theta\), so \(\tan\theta = \mu_s\). With \(\mu_s = 0. 6\), the largest angle is \(\theta = \arctan(0.
Detailed Explanation
Static friction stops the block when the downhill pull is just equal to the friction force that can act. Other options are incorrect because Some think the block can stay on the 45° incline itself because the slope is 45°; A few students guess 60° because they confuse the coefficient with a direct angle.
Key Concepts
Angle of Incline Impact
Static Friction Coefficient
Topic
Friction Forces Analysis
Difficulty
medium level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1An object with a mass of 10 kg is resting on a ramp inclined at 30 degrees. If the coefficient of static friction between the object and the ramp is 0.5, what is the maximum static frictional force that can act on the object before it begins to slide down the ramp?
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2
Question 2A block of metal is placed on an inclined plane with a surface roughness that is significantly higher than that of the plane's opposing surface. If the angle of incline is 30 degrees, what effect does this combination of surface roughness and angle have on the maximum static friction experienced by the block?
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3
Question 3A 5 kg block is placed on a ramp inclined at an angle of 30 degrees. What is the maximum static frictional force that can act on the block if the coefficient of static friction between the block and the ramp is 0.4?
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4
Question 4A 15 kg box is resting on a ramp inclined at 40 degrees. If the coefficient of static friction between the box and the ramp is 0.5, what is the maximum angle of inclination at which the box can remain at rest without sliding down?
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5
Question 5If an object is resting on a surface and begins to slide at a weight of 270 grams, what can you infer about the static friction coefficient between the object and the surface?
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