Problem 4.1:
A particle, starting at the origin, experiences a variable force defined by
F(x) = 3x2, causing it to move along the x-axis. How much work is done on the
particle from its starting point to x = 5?
[Solution]
Problem 4.2:
A 2 kg mass is attached to a spring. The mass is at x = 0 when the spring is
relaxed (not compressed or stretched). If the mass gets displaced from the
equilibrium point (x = 0) then it experiences a force from the spring described
by Fs = - kx, where k is a spring constant. The minus sign indicates that the
force always points towards the equilibrium point, or away from the displacement
of the mass.
From the equilibrium point, the mass on the spring is displaced a distance of 1
meter, then allowed to oscillate on the spring. Using our formula for work from
variable forces, and the Work Energy Theorem, find the velocity of the mass when
it returns to x = 0 after being initially displaced. let k = 200 N/m.
Initial Displacement of Mass
[Solution]
[Solution]
