Concept explainers
(a)
The speed of block if the horizontal surface is frictionless.
(a)
Answer to Problem 15P
The speed of block if the horizontal surface is frictionless is
Explanation of Solution
Draw the figure fir the system as shown below.
In this system block is pulled to some distance and then released from rest, so string comes back to its normal position.
Write the expression for elastic energy stored in the spring as.
Here,
Write the expression for work done by the spring on the block.
Here,
Write the expression for kinetic energy of the system.
Here,
Write the expression for change in kinetic energy of the system.
Here,
As energy of the system is conserved, therefore work done by the string is equal to change in kinetic energy.
Write the expression for change conservation of energy for the system.
Substitute
Value of stretch at final position is zero as string comes to normal state and initial velocity is also zero.
Substitute
Rearrange the above equation for
Conclusion:
Substitute
Thus, the speed of block if the horizontal surface is frictionless is
(b)
The speed of block if there is some friction between block and surface.
(b)
Answer to Problem 15P
The speed of block if there is some friction between block and surface is
Explanation of Solution
Draw the figure for the system considering some friction as shown below.
Friction force results in an increase in internal energy of the block-surface system.
Write the expression for the normal reaction force experience by the block.
Here,
Write the expression for friction force.
Here,
Substitute
Here,
Write the expression for total internal energy.
Here,
Substitute
Work done by string is total of change in kinetic energy and internal energy.
Write the expression for change conservation of energy for the system.
Rearrange the above equation.
Substitute
Value of stretch at final position is zero as string comes to normal state and initial velocity is also zero.
Substitute
Rearrange above equation for
Conclusion:
Substitute
Thus, the speed of block if there is some friction between block and surface is
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Chapter 8 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P8.35. (a) The block is pulled to a position xi = 6.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through equilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position xi/2 = 3.00 cm? (d) Why isnt the answer to part (c) half the answer to part (b)? Figure P8.35arrow_forwardAn inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?arrow_forwardAn inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P7.47. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest? Figure P7.47 Problems 47 and 48.arrow_forward
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