A vertical rope is attached to an object that has a mass of 40.0 kg and is at rest.The tension in the rope needed to give the object an upward speed of 3.50 m/s in 0.700 s is
A)592 N
B)390 N
C)200 N
D)980 N
E)720 N

Question

Quizplus · Accepted Answer

To calculate the tension in the rope, we need to consider both the force needed to overcome gravity and the force needed to accelerate the object upwards. The force to overcome gravity (weight) is given by $F_g = mg$, where $m = 40.0 \, \text{kg}$ is the mass of the object and $g = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity. This gives us $F_g = 40.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 392 \, \text{N}$.To find the force needed to accelerate the object, we use Newton's second law, $F = ma$, where $a$ is the acceleration. The acceleration can be found using the formula $a = \frac{\Delta v}{\Delta t}$, where $\Delta v = 3.50 \, \text{m/s}$ is the change in velocity and $\Delta t = 0.700 \, \text{s}$ is the time taken. This gives us $a = \frac{3.50 \, \text{m/s}}{0.700 \, \text{s}} = 5.00 \, \text{m/s}^2$. The force needed to accelerate the object is then $F_a = 40.0 \, \text{kg} \times 5.00 \, \text{m/s}^2 = 200 \, \text{N}$.The total tension in the rope is the sum of these two forces: $T = F_g + F_a = 392 \, \text{N} + 200 \, \text{N} = 592 \, \text{N}$.

A Vertical Rope Is Attached to an Object That Has