Question

The work used to write an equivalent equation for what can you conclude about the work?

1) the work was completed correctly.
2) both sides needed to be multiplied by 3, rather than divided by 3.
3) when dividing 36 by 3, the answer should have been 1/12, not 12.
4) both terms on the right side need to be divided by 3, not just the 36.

Answer 1

The provided problem suggests a need to check an equation rewritten through division, wherein it is crucial to apply the operation to each term on either side to maintain balance. Verifying the reasonableness of the results in physics ensures principles like conservation of energy are used correctly.

Step-by-step explanation:

A common mathematics task is to manipulate an equation so that it remains in balance, preserving the equality. When rewriting an equation, performing the same operation on both sides is crucial to maintain this balance. In the provided problem, if an equation has multiple terms on one side, and you decide to multiply or divide by a number, you must apply this operation to each term within that side.

If, for example, there is a need to divide both sides of an equation by 3, and one side is a sum like (a + b), then both a and b must be divided by 3, not just one of the terms. An error in division, such as dividing 36 by 3 and getting 1/12, is an arithmetic mistake and not consistent with the standard rules of operation. The division of 36 by 3 should correctly yield 12.

After solving problems involving work and energy, it is important to step back and verify the reasonableness of the result. In physics problems, ensuring that the conservation of energy principles has been applied correctly and that calculations lead to plausible numerical values is a step that should not be overlooked. This includes checking the signs for work done against forces such as friction, as well as making sure the potential energy results make sense within the context of the problem.