A construction crane's cable lifts a 49.5-kg box upward with an acceleration of 1.30 m/s2. Find the tension in the rope.
N
549.945
T = M*g + M*a
To find the tension in the rope, we 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. In this case, the net force acting on the box is equal to the tension in the rope.
Given:
Mass of the box (m) = 49.5 kg
Acceleration (a) = 1.30 m/s^2
Using the equation F = ma, where F is the net force and m is the mass, we can substitute the given values to solve for the tension (F).
F = m * a
F = 49.5 kg * 1.30 m/s^2
F ≈ 64.35 N
Therefore, the tension in the rope is approximately 64.35 N.
To find the tension in the rope, we can use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the mass of the object times its acceleration.
In this case, the net force acting on the box is equal to the tension in the rope minus the force due to gravity. Since the box is being lifted upwards, the net force is equal to the product of the mass of the box and its upward acceleration.
Let's break it down step by step:
1. Find the force due to gravity:
The force due to gravity can be calculated using the equation F = m * g, where F is the force due to gravity, m is the mass of the box, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass of the box is 49.5 kg.
F = 49.5 kg * 9.8 m/s^2 = 485.1 N
2. Calculate the net force:
The net force is equal to the product of the mass of the box and its upward acceleration.
Net force = m * a
= 49.5 kg * 1.3 m/s^2 = 64.35 N
3. Calculate the tension in the rope:
Since the net force is the difference between the tension in the rope and the force due to gravity, we can write the equation as:
Tension - Force due to gravity = Net force
Tension - 485.1 N = 64.35 N
Now, we can solve for the tension:
Tension = Net force + Force due to gravity
= 64.35 N + 485.1 N
= 549.45 N
Therefore, the tension in the rope is 549.45 N.