Question

A crate having a mass of 750kg is lifted from rest with a uniform acceleration by a crane such that after 10 seconds it has a velocity of 14m/s. Calculate the tension in the lifting cable.

Specific requirements:
show and include all calculations and assumptions.

show all units.

Answer 1

A crate having a mass of $750\,\mathrm{kg}$ is lifted from rest with a uniform acceleration by a crane such that after 10 seconds it has a velocity of $14\,\mathrm{m/s}$. Calculate the tension in the lifting cable. Please show and include all calculations and assumptions.

First of all we need to find acceleration of the crate:

$$a = \frac{v}{t}$$

Use second Newton's law:

$$T - F_g = M a$$ $$T = F_g + M a = M g + M a = M \left(g + \frac{v}{t}\right)$$ $$T = 750\,\mathrm{kg} * \left(9.8\,\mathrm{m/s^2} + \frac{14\,\mathrm{m/s}}{10\,\mathrm{s}}\right) = 8400\,\mathrm{N}$$

Answer: $T = 8400\,\mathrm{N}$