Final answer:
The pot will slide because the force of gravity along the inclined plane exceeds the maximum static friction force. By calculating net force and using Newton's second law, we can determine the acceleration of the pot once it begins to slide.
Step-by-step explanation:
The question is asking whether a 2.00 kg copper pot will slide if it is placed on a glass shelf angled at 35.0° to the horizontal and, if so, what would be its acceleration. To determine if the pot will slide, we need to consider the forces acting on it, particularly the force of gravity along the plane, and the maximum static friction force which opposes this motion.
The force of gravity acting down the incline can be calculated using mg sin(θ), while the maximum static friction force can be calculated by μs N, where N is the normal force and is equal to mg cos(θ). By comparing the force of gravity on the incline to the maximum static friction, we can determine whether the pot will slide.
Let's calculate the forces:
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- Force of gravity along the plane: mg sin(35.0°)
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- Maximum static friction force: μs mg cos(35.0°)
For a 2.00 kg copper pot:
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- Fgravity = (2.00 kg)(9.8 m/s2) sin(35.0°) = 11.314 N (approximately)
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- Fstatic friction max = 0.68 × (2.00 kg)(9.8 m/s2) cos(35.0°) = 11.197 N (approximately)
Since the force of gravity along the plane is greater than the maximum static friction force, the pot will indeed slide. Now, to find the acceleration of the pot, we use the formula for net force, Fnet = ma, where a is acceleration, m is mass, and Fnet is the difference between the gravitational force down the plane and the kinetic friction force. The kinetic friction force can be calculated with μk mg cos(θ).
So:
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- Fkinetic friction = 0.53 × (2.00 kg)(9.8 m/s2) cos(35.0°)
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- Fnet = Fgravity - Fkinetic friction
Finally, we can solve for the acceleration a:
Thus, the correct answer is (a) Yes, the pot will slide, and we can calculate its acceleration with the given coefficients and mass.