How much work is required to lift an object with a mass of 5.0 kilograms to a height of 3.5 meters?
A. 17 joules
B. $17 \times 10^?$ joules
C. $1.9 \times 10^2$ joules
D. $1.8 \times 10^2$ joules
Answer (1)
Identify the given values: mass m = 5.0 kg, height h = 3.5 m, and acceleration due to gravity g = 9.8 m / s 2 .
Apply the formula for work done against gravity: W = m g h .
Substitute the values into the formula: W = ( 5.0 ) ( 9.8 ) ( 3.5 ) = 171.5 joules.
The work required is 171.5 joules, which is approximately 1.7 × 1 0 2 joules. The closest option is C. 1.9 × 1 0 2 joules. Therefore, the final answer is 1.9 × 1 0 2 joules .
Explanation
Understanding the Problem We are given the mass of an object ( m = 5.0 kg) and the height ( h = 3.5 m) to which it is lifted. We need to find the work required to lift the object. The work done against gravity is given by the formula W = m g h , where g is the acceleration due to gravity, which is approximately 9.8 m / s 2 .
Substituting the Values Now, we substitute the given values into the formula: W = ( 5.0 kg ) ( 9.8 m/s 2 ) ( 3.5 m ) .
Calculating the Work Calculating the work done: W = 5.0 × 9.8 × 3.5 = 171.5 joules.
Finding the Answer The work required to lift the object is 171.5 joules, which can be written as 1.715 × 1 0 2 joules. Comparing this to the given options, the closest answer is C. 1.9 × 1 0 2 joules.
Examples
Lifting objects is a common task, and understanding the work required is crucial in many fields. For example, construction workers need to know how much energy is required to lift materials to a certain height. Similarly, engineers designing elevators need to calculate the work done by the motor to lift the elevator car and its passengers. In physics, this concept is fundamental to understanding energy and its transfer. If you are lifting a 5 kg bag of groceries to a height of 3.5 meters, you are doing 171.5 joules of work against gravity. This concept applies to various real-world scenarios where objects are lifted against gravity.
