A block slides from rest along a track with an elevated left end and a flat cent

Question

A block slides from rest along a track with an elevated left end and a flat central part into a relaxed spring, as shown in the figure. The curved portion of the track is frictionless, as well as the first portion of the flat part of L = 10 cm. The coefficient of kinetic friction between the block and the only rough part, D = 10 cm, is given by uk = 0.20. Let the initial height of th block be h = 40 cm, its mass be m = 2.5 kg, and the spring constant k = 320 N/m.

Assuming the block compresses the spring by x, find

(i) The work done by the spring force

(j) The compression distance x of the spring.

A block slides from rest along a track with an elevated left end and a flat central part into a relaxed spring, as shown in the figure. The curved portion of the track is frictionless, as well as the first portion of the flat part of L = 10 cm. The coefficient of kinetic friction between the block and the only rough part, D = 10 cm, is given by uk = 0.20. Let the initial height of th block be h = 40 cm, its mass be m = 2.5 kg, and the spring constant k = 320 N/m. Assuming the block compresses the spring by x, find (i) The work done by the spring force (j) The compression distance x of the spring.

Explanation / Answer

energy of the system when spring is not compressed= potential energy of block + potential energy of spring= mgh + 1/2 kx^2 + F.L

=2.5 * 9.8 *(0.40 +0.1)

for state 2, since the package is stopped now

E= 1/2 Kx^2

equating both equations

1/2 kx^2= mg(h +L)- fkd

1/2 * 320* x^2=2.5 * 9.8 *(0.40 +0.1)- 0.20 *x

solving the quadratic equatio we get x= 0.27 m

(a) work done by spring force= 1/2 * 320 *0.27^2

=11.98 J

(b) x= 0.27 m

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