a box of mass 36.5 kg is lifted using a rope. if the acceleration of the box, a, is 3.4 m/s^2(upward), what is the tension in the rope, T?

To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the tension in the rope.

The formula is given as:

T - mg = ma

Where:
T = tension in the rope
m = mass of the box
g = acceleration due to gravity (approximately 9.8 m/s^2)
a = acceleration of the box

Substituting the given values:

T - (m)(g) = (m)(a)

T - (36.5 kg)(9.8 m/s^2) = (36.5 kg)(3.4 m/s^2)

T - 357.7 N = 124.1 N

Now, we can solve for T by adding 357.7 N to both sides of the equation:

T = 481.8 N

Therefore, the tension in the rope, T, is equal to 481.8 N.

To find the tension in the rope, you can use Newton's Second Law of Motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. Mathematically, this can be written as:

F = m * a

Where:
F is the net force acting on the object,
m is the mass of the object,
a is the acceleration of the object.

In this case, the net force is provided by the tension in the rope, T. Therefore, we can rewrite the equation as:

T = m * a

Substituting the given values:
m = 36.5 kg (mass of the box)
a = 3.4 m/s^2 (acceleration)

T = 36.5 kg * 3.4 m/s^2

Now, calculate the tension in the rope:

T = 124.1 N

Therefore, the tension in the rope is 124.1 N (upward).

T = ma = 36.5 * 3.4 = 124.1N.