A mass is attached to a horizontal spring as shown below. The mass (2 kg) is pus

Question

A mass is attached to a horizontal spring as shown below. The mass (2 kg) is pushed to the left, compressing the spring (constant 320 N/m) 20 cm, and held at rest. It is then released. Determine how fast the mass is travelling when the spring is stretched by 15 cm.


0.5 kg mass is connected to the lower end of an ideal vertical coil spring suspended from a retort stand. The mass is held at rest with the spring completed unstretched and then allowed to fall. If the spring constant is 20 N/m, determine the maximum distance the mass drops before coming momentarily to rest and starting up again. Ignore frictional losses. (50 cm)

In the problem above, the mass is now held initially at rest at a position where the spring is stretched 20 cm. Determine the maximum distance the mass will fall.

Explanation / Answer

you should have posted them separately. many questions in single post is not allowed.any way am answering first 2 ,just wrote equation for the third one

potential energy stored in the spring initially PE1 = .5kx^2 = .5*320*.2^2 = 6.4 J
initial Kinetic energy KE1 = 0
at x = .15 PE2 = .5*320*.15^2 = 3.6 J
KE1 + PE1 = KE2 + PE2
KE2 = 2.8 J
.5MV^2 = 2.8
V= 1.6733 m/s

gravitational PE loss = KE + PE of spring

KE = 0 as it is momentarly at rest

mgx = .5kx^2

maximum distance the mass drops before coming momentarily to rest and starting up again x = .7 m = 70 cm

mgx' +.5k.2^2= .5k(x'+.2)^2

solving this you will get the answer

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