The mass of an elevator plus occupants is 752 kg, The tension in the cable supporting the...

Question:

The mass of an elevator plus occupants is 752 kg, The tension in the cable supporting the elevator is 8950 N. What is the unbalanced force? What is the elevator's acceleration?

Newton's Second Law of Motion

The second law of motion depicts that if an unbalanced force is applied on a system then this force will produce an acceleration in the system which magnitude can be obtained by the ratio of the force and the mass of the system.

Answer and Explanation:


Given data:

  • The mass of the elevator is: {eq}m = 752\;{\rm{kg}} {/eq}
  • The tension in the cable is: {eq}T = 8950\;{\rm{N}} {/eq}


Write the expression for the unbalanced force.

{eq}F = T - mg {/eq}

Here, the acceleration due to gravity is {eq}g\left( {9.81\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{\rm{se}}{{\rm{c}}^2}}}} \right. } {{\rm{se}}{{\rm{c}}^2}}}} \right) {/eq}.


Substitute the values in the above equation.

{eq}\begin{align*} F &= 8950 - 752 \times 9.81\\ F &= 1572.88\;{\rm{N}} \end{align*} {/eq}


Thus the unbalanced force is {eq}\color{blue}{1572.88\;{\rm{N}}} {/eq}


This force will cause acceleration in the elevator which magnitude is equal to,

{eq}a = \dfrac{F}{m} {/eq}


Substitute the values in the above equation.

{eq}\begin{align*} a &= \dfrac{{1572.88}}{{752}}\\ a& = 2.09\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^2}}}} \right. } {{{\rm{s}}^2}}} \end{align*} {/eq}


Thus the acceleration of the elevator is {eq}\color{blue}{2.09\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^2}}}} \right. } {{{\rm{s}}^2}}}} {/eq}.


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