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 quantities

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 done against gravity

The force required to lift the object at a constant speed is equal to its weight:

$$F_g = m \cdot g$$

The work done against gravity is the product of this force and the vertical displacement:

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

Calculate the numerical value of the work

Substitute the given values into the work formula:

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

$$W = 98\text{ J}$$

Match the result with the options

The calculated work is \(98\text{ J}\), which corresponds to option D.

Answer:

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