Select the correct answer.
A forklift raises a crate weighing $8.35 \times 10^2$ newtons to a height of 6.0 meters. What amount of work does the forklift do?
A. $2.5 \times 10^3$ joules
B. $5.0 \times 10^3$ joules
C. $2.4 \times 10^4$ joules
D. $4.9 \times 10^4$ joules
Answer (1)
The problem requires calculating the work done by a forklift.
The formula for work is W = F × d , where F is force and d is distance.
Substitute the given values: W = ( 8.35 × 1 0 2 ) × 6.0 = 5010 joules.
Express the answer in scientific notation: 5.0 × 1 0 3 joules .
Explanation
Understanding the Problem We are given that a forklift raises a crate weighing 8.35 × 1 0 2 newtons to a height of 6.0 meters. We need to find the amount of work done by the forklift.
Stating the Formula The formula for work done is given by:
W = F × d
where:
W is the work done (in joules)
F is the force applied (in newtons)
d is the distance over which the force is applied (in meters)
Identifying the Values In this problem, the force is the weight of the crate, which is 8.35 × 1 0 2 newtons, and the distance is the height to which the crate is raised, which is 6.0 meters.
Calculating the Work Done Substitute the given values into the formula:
W = ( 8.35 × 1 0 2 ) × 6.0
W = 835 × 6.0
W = 5010 joules
Expressing in Scientific Notation Now we need to express the result in scientific notation and compare it with the given options.
W = 5010 joules = 5.01 × 1 0 3 joules
Comparing this with the given options, we see that option B is the closest.
Final Answer The amount of work done by the forklift is 5.01 × 1 0 3 joules. The closest answer among the options is 5.0 × 1 0 3 joules.
Examples
Work is a fundamental concept in physics and engineering. For example, when designing a crane to lift heavy materials on a construction site, engineers need to calculate the work done by the crane's motor to ensure it can lift the load to the required height. This involves considering the weight of the materials (force) and the height to which they need to be lifted (distance). By accurately calculating the work, engineers can select the appropriate motor and ensure the crane operates efficiently and safely. Understanding work also helps in optimizing energy consumption and reducing operational costs.
