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Concept explainers
(a) What is the smallest force parallel to a
(a)
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The magnitude of the minimum force required to keep the
Answer to Problem 80SP
Solution:
Explanation of Solution
Given data:
The weight of the objectis
Coefficient of static friction and kinetic friction between the object and
Formula used:
Write the expression of the coefficient of static friction:
Here,
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Consider,
Draw the free body diagram of the object:
In the above diagram,
Recall the expression for the first condition of the force’s equilibrium:
Considering along the perpendicular to the inclined plane, the direction of the upward forces is positive and the direction of the downward forces is negative. Therefore,
Here, considering coefficient of the static friction force because the object is just sliding down.
Recall the expression of static friction force:
Substitute
Understand that the acceleration of the object will be zero because it will be at rest after the application of force
Rewrite the expression for the first condition of the force’s equilibrium:
Considering along the parallel to the inclined plane, the direction of the rightward forces is positive and the direction of the leftward forces is negative. Therefore,
Substitute
Conclusion:
Therefore, the magnitude of the minimum force required to keep the object from sliding down the incline plane is
(b)
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The magnitude of the forceapplied parallel to the
Answer to Problem 80SP
Solution:
Explanation of Solution
Given data:
The weight of the object is
Coefficient of static friction and kinetic friction between the object and
The acceleration of the blockis zero because its moves with constant velocity.
Formula used:
Write the expression of the coefficient of static friction:
Here,
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Since the
Draw the free body diagram of the object:
In the above diagram,
The object is moving with constant velocity.
Rewrite the expression for the first condition of the force’s equilibrium.
Considering along the parallel to the inclined plane, the direction of the rightward forces is positive and the direction of the leftward forces is negative. Therefore,
Substitute
Conclusion:
Therefore, the magnitude of the parallel force needed to keep the objectmoving up the inclineat a constant speed is
(c)
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The magnitude of the acceleration of an object if a
Answer to Problem 80SP
Solution:
Explanation of Solution
Given data:
The weight of the object is
Parallel pushing force is 94N.
Coefficient of static friction and kinetic friction between the object and incline is
Formula used:
Write the expression of the coefficient of the kinetic friction:
From the Newton’s second law of the motion, the expression of the force is
Here,
Write the expression for the weight of the
Here,
Explanation:
Since the
Draw the free body diagram of the object:
In the above diagram, considering the objectup the incline,
Here, considering the coefficient of the kinetic friction because
Recall the expression of coefficient of kinetic friction:
Here,
Substitute
Recall the expression for the weight of the
Substitute
Recall the expression for Newton’s second law of the motion:
Considering along the parallel to the inclined plane, the direction of the rightward forces is positive and the direction of the leftward forces is negative. Therefore,
Here,
Substitute
Conclusion:
Therefore, the magnitude of the acceleration of the object is
(d)
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Thedistance coveredby the object after
Answer to Problem 80SP
Solution:
Explanation of Solution
Given data:
The weight of the object is
Coefficient of static friction and kinetic friction between the object and incline is
Time to considered is
Initial velocity is
Formula used:
Write the expression of the displacement:
Here,
Explanation:
Recall the expression of the displacement:
Substitute
Conclusion:
The displacement of the object is
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