14.3 As shown in the figure below, a box of mass m 15.3 kg is released from rest

Question

14.3

As shown in the figure below, a box of mass m 15.3 kg is released from rest (at position A) at the top of a 30.0 frictionless incline. The box slides a distance d 4.30 m down the incline before it encounters (at position B) a spring and compresses it an amount xc 0.240 m (to point C) before coming momentarily to rest. Using energy content, determine the following point of release (a) speed of the box at position B m/s VB, (b) spring constant N/m (c) the physical quantity that is constant throughout the process kinetic energy O elastic potential energy O gravitational potential energy O total energy Tutorial

Explanation / Answer

For these problems, the easiest method is to use conservation of mechanical energy, since there is no friction

.a ) punto A

EmA = K + U

K=0 U = mgh

like this in an inclined plane we can use trigonometry to find pair up

Tg = h/ 4.30 h = 4.30 tg

Poimt B

EmB = K + U

U=0 reference at this point

EmA = EmB

mg 4.30 tg = ½ m v2

v2= 2g 4.30 tg 30 v2= 48.66

V = 6.976 m/s

.b) We write the energy in points B y C

point B

EmB = K + Ug+Ur

K= ½ m V2

Ug = mg h´ tg = h´/0.240 We write the energy in points

Ur= ½ k x2 x=0 uncompressed spring

Point C

Emc = Ur

stionary and zero block system refencia

EmC = ½ K x2

EmB = EmC

½ m V2 + m g 0.240 Tg 30 = ½ K x2

K= (½ m V2+ m g 0.240 Tg 30 )2/x2

K = ( ½ 15.3 6.9762+ 15.3 9,8 0.250 Tg 30) 2/0,242= (372.28+ 21.64) *34.72

K = 13676 N/m

.c) As we saw energy transformed, but the sum (ENERGY total) remains constant throughout the process, so the total energy is the answer

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