Question

A block of mass m= 5.00-kg is moving to the right with a speed of v= 2.00 m/son a horizontal,frictionless surface. The block encounters a relaxed(that is, neither compressed nor extended)spring with spring constant k= 2,000.00 N/m.

a.What is the kinetic energy of the block before hitting the spring?

b.What is the kinetic energy of the block when the spring is at maximum compression?

c.How much energy is stored in the spring at maximum compression?

d.How far does the spring compress at its maximum compression?

e.If the spring converts its stored energy completely into motion of the block, what is the speedof the blockafter release from the spring?

f.(For this part of the problem,the surface is not frictionless) Suppose the speed of the block after release from the spring is 1.5 m/s to the left, how much work (sign and magnitude) was done by non-conservative forces between the time when the initial velocity is 2.00 m/s and the time when the velocity = -1.50 m/s?

Answer 1

Mass of the block = 5kg; velocity = 2m/s; spring constant k=2000N/m

a)Kinetic energy is the energy possessed by a body due to its motion, it is mathematically defined as,

velocity before hitting the spring is 2m/s, so,

K.E = 0.5*5*2*2 J

= 10J

b) At maximum compression, all the kinetic energy is converted into potential energy, thus at maximum compression the kinetic energy is zero

c)Energy stored in the spring at maximum compression is the Kinetic energy when the block just touched the spring (it is due to conservation of energy)

thus, energy stored at max compression = 10J

d) If a spring with spring constant k is compressed by a distance x then the energy stored in the spring is given as,

We know from conservation of energy,

Enerygy stored in spring at maximum compression = K.E of the mass

Spring is compressed by 10cm.

e) If this stored energy is converted to the motion of the block then this energy will be converted to the kinteic energy of the block,i.e,

is the velocity of the block when it is released.

Speed of block when released from the spring is 2m/s

f)Since there is friction some the energy will be used up by it.

From work-energy theorem, Work done is equal to chenge is kinetic energy

is the final velocity after release of block

is the initial velocity before hitting the spring

Work done by non-conservative forces between the time when the initial velocity is 2.00 m/s and the time when the velocity -1.50 m/s is -4.375J