A 400-kg box is lifted vertically upward with constant velocity by means of two cables pulling at 40.0° on either side of the vertical direction. What is the tension in each cable?
A) 2560 N
B) 231 N
C) 400 N
D) 800 N
E) 3920 N

Question

Quizplus · Accepted Answer

The tension in each cable can be found by analyzing the forces acting on the box. Since the box is moving with constant velocity, the net force acting on it is zero. This means the upward forces (the vertical components of the tension in the cables) must balance the downward force of gravity on the box.The gravitational force acting on the box is $F_g = mg = 400 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 3920 \, \text{N}$.Let $T$ be the tension in each cable. The vertical component of the tension can be found using trigonometry, specifically $T \cos(40^\circ)$ for each cable. Since there are two cables, the total upward force is $2T \cos(40^\circ)$.Setting the upward force equal to the gravitational force gives:$$2T \cos(40^\circ) = 3920 \, \text{N}$$Solving for $T$ gives the tension in each cable. Given the choices, the correct tension that balances this equation is $T = 2560 \, \text{N}$, which corresponds to choice A.

A 400-Kg Box Is Lifted Vertically Upward with Constant Velocity