Question

A 74.5 kg student (initially at rest) climbs a rope in gym class to a vertical height of 3.31 m in 2.79 s and has a final speed of 2.25 m/s at that height.

What is the total energy (work) of the student at the 3.31 m height?

Answer 1

To calculate the total energy of a student at a certain height, add the kinetic energy (KE) and the potential energy (PE). For a 74.5 kg student who reached a height of 3.31 m with a speed of 2.25 m/s, the total energy is 2605.54 joules (J).

Step-by-step explanation:

To determine the total energy (work) of the student at a height of 3.31 m, we need to consider both the kinetic energy (KE) and the potential energy (PE) at that height. The total mechanical energy (E) is the sum of KE and PE, given by the formulas:

• KE = (1/2)mv²
• PE = mgh

Where m is the mass of the object, v is the final speed, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height above the reference point. For the 74.5 kg student, the calculations are as follows:

• KE = (1/2)(74.5 kg)(2.25 m/s)² = 188.44 J
• PE = (74.5 kg)(9.81 m/s²)(3.31 m) = 2417.10 J

Therefore, the total energy at the height of 3.31 m is:

E = KE + PE = 188.44 J + 2417.10 J = 2605.54 J