At one instant, a mass (m = 1.3 kg) is at the location < 0.42, -0.33, 0 >m and a

Question

At one instant, a mass (m = 1.3 kg) is at the location < 0.42, -0.33, 0 >m and attached to one end of a spring with a spring constant ks = 60 N/m and a relaxed length L0 = 0.22 m. The origin is located where the other end of the spring attaches to the ceiling.

A ball is attached to the end of a spring. The spring is attached to the ceiling. The spring is hanging at an angle from vertical.

(a) Determine the force acting on the mass due to the spring.
F{spring}= <_,_,_> N

(b) Determine the net vector force acting on the mass.
F{net}=<_,_,_> N

any help would be very appreciated!

Explanation / Answer

Distance of mass from origin D = (.42^2 + .33^2)^1/2 = .534 m Elongation of spring x = D - .22 = .31 m F = - K x = 60 * .31 = -18.8 N Now just draw a force diagram with the mass at the origin Tan theta = -.33 / .42 theta = 38.2 deg below x-axis Fx = -18.8 cos 38.2 = -14.8 N directed to left Fy = 18.8 sin 38.2 - m g = 11.6 - (1.3 * 9.8) = -1.14 N downwards Now just find the resultant force and direction

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