Question

A block of mass m is launched by a spring of stiffness k up an incline at angle ? to the horizontal. The spring is initially compressed a distance s, and the block is released from rest. It moves a distance d along the incline, opposed by a constant frictional force f, and leaves the ramp with final speed v. Consider the energy balance in the process. Write out a relation among the initial and final potential energies in the spring, gravitational potential energies of the block, kinetic energies of the block, and the mechanical energy dissipated (converted to thermal energy) by friction. Write this out in words (or abbreviations); the algebra is the next part. a) Replace each energy term by an algebraic expression to obtain an energy-balance equation. Solve to express the final speed v in terms of the other quantities. b) Now take m = 0.20 kg, k = 48 N/m, f = 0.50 N, d = 1.2 m, ? = 37°, s = 0.40 m, and get a numerical value for the final speed.

          A block of mass m is launched by a spring of stiffness k up an incline at angle ? to the horizontal. The spring is initially compressed a distance s, and the block is released from rest. It moves a distance d along the incline, opposed by a constant frictional force f, and leaves the ramp with final speed v.

Consider the energy balance in the process. Write out a relation among the initial and final potential energies in the spring, gravitational potential energies of the block, kinetic energies of the block, and the mechanical energy dissipated (converted to thermal energy) by friction. Write this out in words (or abbreviations); the algebra is the next part.

a) Replace each energy term by an algebraic expression to obtain an energy-balance equation. Solve to express the final speed v in terms of the other quantities.

b) Now take m = 0.20 kg, k = 48 N/m, f = 0.50 N, d = 1.2 m, ? = 37°, s = 0.40 m, and get a numerical value for the final speed.

A block of mass m is launched by a spring of stiffness k up an incline at angle ? to the horizontal. The spring is initially compressed a distance s, and the block is released from rest. It moves a distance d along the incline, opposed by a constant frictional force f, and leaves the ramp with final speed v.

Consider the energy balance in the process. Write out a relation among the initial and final potential energies in the spring, gravitational potential energies of the block, kinetic energies of the block, and the mechanical energy dissipated (converted to thermal energy) by friction. Write this out in words (or abbreviations); the algebra is the next part.

a) Replace each energy term by an algebraic expression to obtain an energy-balance equation. Solve to express the final speed v in terms of the other quantities.

b) Now take m = 0.20 kg, k = 48 N/m, f = 0.50 N, d = 1.2 m, ? = 37°, s = 0.40 m, and get a numerical value for the final speed.

Added by Justin C.

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