Chapter 5, Problem 1WUE

Physics Review A crane lifts a loud of bricks of mass 1 570 kg at an initial acceleration of 1.60 m/s² Calculate the tension in the cable. (See Section 4.5.)

To determine

The tension in the cable.

Answer to Problem 1WUE

Solution:

The tension in the cable is $\text{1}\text{.79}\times {\text{10}}^4\text{N}$.

Explanation of Solution

Given Info:

The mass of the load is $1570\text{kg}$ , $9.80\text{m}/{\text{s}}^{\text{2}}$ and the acceleration of the load is $1.60\text{m}/{\text{s}}^{\text{2}}$.

Write balancing equation of the total external force on the load using Newton’s second law.

$ma=T-mg$

• m is the mass of the load
• T is the tension on the cable
• g is the acceleration due to gravity

Rewrite the above equation in terms of tension on the string.

$\begin{array}{c}T=ma+mg\\ =m(g+a)\end{array}$

Substitute $1570\text{kg}$ for m , $9.80\text{m}/{\text{s}}^{\text{2}}$ for g and $1.60\text{m}/{\text{s}}^{\text{2}}$ for a to calculate T.

$\begin{array}{c}T=\left(1570\text{kg}\right)\left(9.80\text{m}/{\text{s}}^{\text{2}}+1.60\text{m}/{\text{s}}^{\text{2}}\right)\\ =17898\text{N}\\ \text{=1}\text{.79}\times {\text{10}}^4\text{N}\end{array}$

Conclusion:

Therefore, the tension in the cable is $\text{1}\text{.79}\times {\text{10}}^4\text{N}$