7.21 As shown in the figure below, two masses m 1 = 5.30 kg and m 2 which has a

Question

7.21

As shown in the figure below, two masses m1 = 5.30 kg and m2 which has a mass 80.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 1.10 m, use energy content to determine the following.

As shown in the figure below, two masses m1 = 5.30 kg and m2 which has a mass 80.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 1.10 m, use energy content to determine the following. speed v of the masses magnitude of the tension T in the cord

Explanation / Answer

m2 travels a distance of h upwards where as m1 travels a distance of h downwards

therefore increase in potential energy

=m1gh-(0.8)m1gh

=0.2m1gh

=0.2*5.3*9.8*1.1

11.4268

both of them move them move with the same speed

there fore total kinetic energy

= m1v^2+0.8*m1*v^2

=1.8m1*V^2

this must be equal to change in potential energy for energy conservation

therefore

11.4268 = 1.8*5.3*v^2

v=1.094m/s

equation of motion of block m1

m1g-t = m1a

equation of motion for block m2

t-0.8m1g = 0.8m1a

t-0.8m1g = 0.8(m1g-t)

1.8t=1.6m1g

t=1.6*5.3*9.8/1.8

t=46.17 N

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