Final answer:
The question involved calculating the height to which a crane lifted a 10000 kg weight using 4 MJ of work. By using the work-energy principle and the formula for work done (W = F × d), we can find the height after determining the weight of the object using the force of gravity to be 4,000,000 J.
Step-by-step explanation:
The problem given is a physics question that involves calculating the height to which a crane lifted a weight using the work done by the crane.
Work done (W) is related to the force (F) applied to move an object through a distance (d) in the direction of the force and is given by the formula W = F × d.
When lifting, the force is equivalent to the weight of the object, which is the mass (m) multiplied by the acceleration due to gravity (g, where g = 9.8 m/s2 on Earth).
For the crane problem, the work done is 4 MJ (mega joules) or 4,000,000 J (joules).
To find the height (h), we rearrange the formula to solve for distance, considering that the force applied is the weight of the object.
First, we calculate the weight of the object (the force due to gravity):
Weight (F) = mass (m) × gravity (g)
= 10000 kg × 9.8 m/s2
= 98000 N (newtons).
Next, we calculate the height using the work done:
Work (W) = Force (F) × Height (h), rearranging for height gives us
Height (h) = Work (W) / Force (F)
= 4,000,000 J / 98000 N
= 4,000,000 J.