Question

1. an object of mass \\(5.0\text{ kg}\\) is lifted vertically upward by \\(2.0\text{ m}\\). assuming the acceleration due to gravity is \\(9.8\text{ m/s}^2\\), how much work is done against gravity?

a. \\(10\text{ j}\\)
b. \\(20\text{ j}\\)
c. \\(49\text{ j}\\)
d. \\(98\text{ j}\\)

Explanation:

Identify the given physical parameters

We extract the values from the problem statement:

• Mass of the object: \(m = 5.0\text{ kg}\)
• Vertical displacement: \(h = 2.0\text{ m}\)
• Acceleration due to gravity: \(g = 9.8\text{ m/s}^2\)

State the formula for work against gravity

The force required to lift the object at a constant velocity is equal in magnitude to its weight:

$$F = m \cdot g$$

The work done by this lifting force over a vertical distance \(h\) is:

$$W = F \cdot h = m \cdot g \cdot h$$

Calculate the numerical value of work

Substitute the given values into the work formula:

$$W = (5.0\text{ kg}) \cdot (9.8\text{ m/s}^2) \cdot (2.0\text{ m})$$

$$W = 49\text{ kg}\cdot\text{m}^2/\text{s}^2 = 49\text{ J}$$

Match the result with the options

The calculated work is \(49\text{ J}\), which corresponds to option C.

Answer:

• (A) 10 J
• (B) 20 J
• (C) 49 J (Correct answer)
• (D) 98 J