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## A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released fro

Question

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:______.

(a) its maximum speed will be 2v and its maximum kinetic energy will be 4K.

(b) its maximum speed will be 2v and its maximum kinetic energy will be √2K.

(c) its maximum speed will be 4v and its maximum kinetic energy will be 2K.

(d) its maximum speed will be 2v and its maximum kinetic energy will be 2K.

(e) its maximum speed will be v √2 and its maximum kinetic energy will be 2K.

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Physics
3 years
2021-08-21T02:27:15+00:00
2021-08-21T02:27:15+00:00 1 Answers
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## Answers ( )

Answer:(a) its maximum speed will be 2v and its maximum kinetic energy will be 4K.

Explanation:The velocity of the load if it were attached would be given by

ωis the angular velocity of the spring,Ais the amplitude andxis the displacement of the load at any time.When the spring is compressed (or extended), then the displacement,

x, is maximum and equal to the amplitude,A. When released, at its equilibrium point,xis zero. It is at this point that the unattached load moves away.Using

x= 0 in the equation,This is the maximum velocity.

ωdepends on the mass of the load and the spring constant; hence it is constant.It follows then that .

When the compression is doubled,

Ais doubled. Because of the linear relationship betweenvandA,vis also doubled.Kinetic energy is given by

When

vis doubled, the kinetic energy becomesThe kinetic energy is multiplied by a factor of 4.