Question

the concepts in this problem are similar to those in multiple-concept example 4, except that the force doing the work in this problem is the tension in the cable. a rescue helicopter lifts a 80.0-kg person straight up by means of a cable. the person has an upward acceleration of 0.742 m/s2 and is lifted from rest through a distance of 12.3 m. (a) what is the tension in the cable? how much work is done by (b) the tension in the cable and (c) the person's weight? (d) use the work-energy theorem and find the final speed of the person.

Answer 1

To calculate the tension in the cable supporting the person, we use Newton's second law. The work done by the tension in the cable and the person's weight can be calculated using the work formula. The final speed of the person can be found using the work-energy theorem.

Step-by-step explanation:

To calculate the tension in the cable, we need to use Newton's second law, which states that the net force acting on an object equals the mass of the object multiplied by its acceleration. In this case, the net force is equal to the tension in the cable minus the weight of the person:

T - mg = ma

Where T is the tension in the cable, m is the mass of the person, g is the acceleration due to gravity, and a is the person's upward acceleration.

To calculate the work done by the tension in the cable, we use the equation:

Work = Force x Distance

where the force is the tension in the cable and the distance is the height the person is lifted. To calculate the work done by the person's weight, we use the equation:

Work = Force x Distance

where the force is the weight of the person and the distance is the height the person is lifted. Finally, to calculate the final speed of the person, we use the work-energy theorem:

Work = Change in Kinetic Energy

where the work is the total work done on the person and the change in kinetic energy is equal to 1/2 m v^2, where m is the mass of the person and v is the final velocity.

Answer 2

To find the tension in the cable lifting a person, use Newton's second law considering weight and cable tension. Calculate the work done by tension and weight by multiplying the respective force by the distance. Apply the work-energy theorem to determine the final velocity of the person.

Step-by-step explanation:

To solve the student's problem regarding the tension in the cable and the related work done, we apply Newton's second law and the work-energy theorem. To find the tension, we consider the forces acting on the person being lifted: gravity (weight) and the tension in the cable. The net force will equal the mass times the acceleration. Using the formula:

• Tension (T) = Weight + (Mass × Acceleration)

where the weight is the force of gravity on the person (mass × gravity), we calculate the tension. For work done:

• Work by tension (Wt) = Tension (T) × Distance
• Work by weight (Ww) = Weight × Distance

And for the final speed using the work-energy theorem:

• Final kinetic energy = Work by tension - Work by weight

From this, we can calculate the final speed using the formula:

• Final velocity (v) = √(2 × Final kinetic energy / Mass)