Final answer:
The tension in the rope holding a 64.0kg box at rest is equal to the gravity force acting on the box, which is 627.2 N.
Step-by-step explanation:
The tension in a rope from which a 64.0kg box hangs at rest can be found using Newton's second law of motion. When the box is at rest, the only forces acting on it are the gravitational force (its weight) and the tension in the rope. The forces are balanced since the box is not moving, implying the tension in the rope is equal to the weight of the box.
The weight (W) is calculated by the formula W = m * g, where m is the mass of the box and g is the acceleration due to gravity (9.8 m/s² on Earth). Plugging in the values:
W = 64.0kg * 9.8 m/s² = 627.2 N
Thus, the tension in the rope is 627.2 Newtons (N), which is also the force needed to hold the box stationary.