Work Done by a Variable Force Along a Line. If a variable force F(x) moves an...

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Work Done by a Variable Force Along a Line. If a variable force F(x) moves an object in a positive direction along the x-axis from x = a to x = b, then the work done on the object is Part 1. Setup the integral that will give the work done by a variable force, F = 2x² N, in moving a particle (along a line) from x = 4 m to x = 10 m. W = Part 2. W = f*F(2) dz a Calculate the done by the force described above. W J. Note: enter your answer as an exact value without using decimals. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that we wish to compress a spring with a natural length of 8 ft to a length of 5 ft with a force constant (or spring constant) of 18. Assuming the spring is laid out along the z-axis with its movable end at the origin and its fixed end at x = 8 ft, how much force is required to compress the spring 3 ft from its natural (unstressed) length? F(3) = lb Part 2. Setup the integral that will give the work done by force, F(x), in compressing the spring from its natural length to a length of 5 ft. -6 W = Part 3. Calculate the work done by the force described above. W foot-pounds. Note: enter your answer as an exact value without using decimals. Work Done by a Variable Force Along a Line. If a variable force F(x) moves an object in a positive direction along the x-axis from x = a to x = b, then the work done on the object is Part 1. Setup the integral that will give the work done by a variable force, F = 2x² N, in moving a particle (along a line) from x = 4 m to x = 10 m. W = Part 2. W = f*F(2) dz a Calculate the done by the force described above. W J. Note: enter your answer as an exact value without using decimals. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that we wish to compress a spring with a natural length of 8 ft to a length of 5 ft with a force constant (or spring constant) of 18. Assuming the spring is laid out along the z-axis with its movable end at the origin and its fixed end at x = 8 ft, how much force is required to compress the spring 3 ft from its natural (unstressed) length? F(3) = lb Part 2. Setup the integral that will give the work done by force, F(x), in compressing the spring from its natural length to a length of 5 ft. -6 W = Part 3. Calculate the work done by the force described above. W foot-pounds. Note: enter your answer as an exact value without using decimals.

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