The system shown in the figure is released from rest. The 4-kg mass slides on th

ID: 1920531 • Letter: T

Question

The system shown in the figure is released from rest. The 4-kg mass slides on the smooth horizontal surface.

(a) Determine the angular speed of the pulley when the 20-kg mass has fallen a distance of h m.

(b) The ange (in degrees) the pulley would turn through during that time. Ignore the pulley mass. The pulley diameter is d.

h[m] = 2.03;

d[m] = 0.203;

Enter your answers below:

A) Pulley speed[rad/s] =

B) Angle of rotation[degrees] =

The system shown in the figure is released from rest. The 4-kg mass slides on the smooth horizontal surface.

(a) Determine the angular speed of the pulley when the 20-kg mass has fallen a distance of h m.

(b) The ange (in degrees) the pulley would turn through during that time. Ignore the pulley mass. The pulley diameter is d.

write newton's second law for each mass

if the mass of the string is negligible and the pulley is frictionless, the tension in the rope is the same throughout

newton's second law for the 4 kg mass is:

T=4a

for the 20 kg mass:

T-20g=-20a (the minus sign indicates the mass is accelerating down)

we subtract these two equations to get:

20g=24a or a = 20/24 g = 5g/6=8.17m/s/s

now, if the 20kg mass started from rest, and we know its accel is 8.17m/s/s, we also know

vf^2=v0^2+2ad

since v0=0, we have vf^2=2(8.17)d or

v=sqrt[16.33d]=4.04sqrt[d]

and this is the speed of the mass after falling (from rest) through a distance of d meters.

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