An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 1820 kg. When that occupant drops a coin, its acceleration relative to the cab is 8.50 m/s2 downward. What is the tension in the cable?

Respuesta :

Answer:

Explanation:

Given

combined mass of cab and occupant is [tex]M=1820\ kg[/tex]

acceleration of coin w.r.t cab is [tex]a_{co,c}=8.50\ m/s^2(downward)[/tex]

we can write

[tex]a_{co,c}+a_{c,g}=a_{co,g}[/tex]

where [tex]a_{co,c}[/tex]=acceleration of coin w.r.t cab

[tex]a_{c,g}[/tex]=acceleration of cab w.r.t ground

[tex]a_{co,g}[/tex]=acceleration of coin w.r.t ground

thus [tex]-8.5+a_{c,g}=-9.8[/tex]

[tex]a_{c,g}=-9.8+8.5[/tex]

[tex]a_{c,g}=-1.3\ m/s^2[/tex] i.e. elevator is moving downward with an acceleration of [tex]1.3 m/s^2[/tex]

Therefore

[tex]T-Mg=Ma_{c,g}[/tex]

[tex]T=M(g+a)[/tex]

[tex]T=1820\cdot (9.8-1.3)[/tex]

[tex]T=1820\times 8.5[/tex]

[tex]T=15,470\ N[/tex]

[tex]T=15.47\ kN[/tex]