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. An elevator cab that weighs 27.8 kN moves upward. What is the tension in the cable if the cab’s speed is (a) increasing at a rate of 1.22 m/s2 and (b) decreasing at a rete of 1.22 m/s2?

Answer :

Explanation:

It is given that, [tex]F_{w}[/tex] = 27.8 kN = [tex]27.8 \times 10^{3} N[/tex]

Now, formula for the mass of elevator is as follows.

              [tex]F_{w} = mg[/tex]

                m = [tex]\frac{F_{w}}{g}[/tex]

                    = [tex]\frac{27.8 \times 10^{3}}{9.8}[/tex]

                    = [tex]2.84 \times 10^{3}[/tex] kg

(a)   When acceleration is increasing at a rate of 1.22 [tex]m/s^{2}[/tex]. Force according to the Newton's second law of motion is as follows.

               F = T - mg = ma

         [tex]T - 27.8 \times 10^{3} = 2.84 \times 10^{3} \times 1.22[/tex]

            T = [tex]31.27 \times 10^{3} N[/tex]

Hence, tension in the cable if the cab’s speed is increasing at a rate of 1.22 [tex]m/s^{2}[/tex] is [tex]31.27 \times 10^{3} N[/tex].

(b)   When acceleration is decreasing at a rate of 1.22 [tex]m/s^{2}[/tex]. Force according to the Newton's second law of motion is as follows.

                      F = T - mg = ma

         [tex]T - 27.8 \times 10^{3} = 2.84 \times 10^{3} \times (-1.22)[/tex]

            T = [tex]24.34 \times 10^{3} N[/tex]

Hence, tension in the cable if the cab’s speed is decreasing at a rate of 1.22 [tex]m/s^{2}[/tex] is [tex]24.34 \times 10^{3} N[/tex].

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