Bank robbers have pushed a 1000 ???????? safe to a second-story floor-to-ceiling window. They plan to break the window, then lower the safe 3.0 m to their truck. They stack up 500 ???????? of furniture, tie a rope between the safe and the furniture, and place the rope over a pulley that is frictionless and massless. They then push the safe out of the window. What is the safe’s speed when it hits the truck if it was initially at rest after being pushed out of the window? The coefficient of kinetic friction between the furniture and the floor is 0.50

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aristocles aristocles · Answer 1 · 2019-10-11T03:03:45+02:00

Answer:

[tex]v_f = 5.42 m/s[/tex]

Explanation:

For the locker which is lowered down the force equation is given as

[tex]Mg - T = Ma[/tex]

for the furniture which is moving on the floor we have

[tex]T - F_f = ma[/tex]

also we know that

[tex]F_f = \mu mg[/tex]

[tex]T - \mu mg = ma[/tex]

now we will have

[tex]Mg - T = Ma[/tex]

[tex]T - \mu mg = ma[/tex]

from above two equations we have

[tex]a = \frac{Mg - \mu mg}{M + m}[/tex]

now plug in all values in it

[tex]a = \frac{(1000 - (0.5\times 500))9.81}{1000 + 500}[tex]

[tex]a = 4.9 m/s^2[/tex]

Now the speed of the locker when it falls by distance d = 3 m

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]v_f^2 - 0 = 2(4.905)(3)[/tex]

[tex]v_f = 5.42 m/s[/tex]