A rope of negligible mass pulls a 38-kg block block vertically upward with a constant acceleration of 6.0 meters per second squared. What is the tension of the rope?
See example 2:
http://www.cliffsnotes.com/study_guide/Dynamics.topicArticleId-10453,articleId-10417.html
M*(g + a) = 38*(9.8 + 6.0)
= 600.4 Netwons
To find the tension in the rope, we need to 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. Tension in the rope is one of the forces acting on the block, so we can use this equation to solve for it.
The net force acting on the block is the difference between the force pulling it upward (tension) and its weight pulling it downward. The weight of the block can be calculated using the equation: weight = mass × gravitational acceleration.
The gravitational acceleration on Earth is approximately 9.8 m/s². So the weight of the block is 38 kg × 9.8 m/s² = 372.4 N.
Now, we can apply Newton's second law to find the tension. The net force is equal to mass × acceleration: net force = mass × acceleration. In this case, the net force is the tension force minus the weight force:
tension - weight = mass × acceleration.
Substituting the values we have:
tension - 372.4 N = 38 kg × 6.0 m/s².
Now, we can solve for the tension:
tension = (38 kg × 6.0 m/s²) + 372.4 N.
tension = 228 kg·m/s² + 372.4 N.
tension = 228 N + 372.4 N.
tension = 600.4 N.
Therefore, the tension in the rope is 600.4 N.