Concept explainers
A block of mass 2.20 kg is accelerated across a rough surface by a light cord passing over a small pulley as shown in Figure P5.51. The tension T in the cord is maintained at 10.0 N, and the pulley is 0.100 m above the top of the block. The coefficient of kinetic friction is 0.400. (a) Determine the acceleration of the block when x = 0.400 m. (b) Describe the general behavior of the acceleration as the block slides from a location where x is large to x = 0. (c) Find the maximum value of the acceleration and the position x for which it occurs. (d) Find the value of x for which the acceleration is zero.
Figure P5.51
(a)
The acceleration of the block when
Answer to Problem 51CP
The acceleration of the block when
Explanation of Solution
The mass of block is
Consider the free body diagram give below.
Figure I
Write the expression for the angle the block makes with the pulley
Here,
Substitute
Write the formula to calculate normal reaction
Here,
Substitute
The equation for the force in x direction
Here,
Conclusion:
Substitute
Therefore, the acceleration of the block when
(b)
The general behavior of the acceleration as the block slides from a location where
Answer to Problem 51CP
The acceleration increases initially then decreases and becomes negative as the value of
Explanation of Solution
Substitute
Substitute
Substitute
Substitute
When
Conclusion:
Therefore, the acceleration increases initially then decreases and becomes negative as the value of
(c)
The maximum value of the acceleration and its corresponding position.
Answer to Problem 51CP
The maximum value of the acceleration is
Explanation of Solution
Differentiate the equation (IV) with respect to
Further solve for
Substitute
Rearrange (I) for
Substitute
Conclusion:
Therefore, the maximum value of the acceleration is
(d)
The position where acceleration is zero.
Answer to Problem 51CP
The acceleration is zero at the position
Explanation of Solution
Substitute
Substitute
Conclusion:
Substitute
Solving the above expression for
Therefore, the position
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Chapter 5 Solutions
PHYSICS FOR SCIENCE & ENGINEERS
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