# Ratios of work to height with same mass

#### michaelw

This is a question from the MCAT, test 3R, and I am stumped as to why the answer is what it is.

"A mass is lifted from the ground to an altitude h1, requiring work W1. The work to lift an identical mass to height h2 is W2. If h2 is twice h1, what is the ratio of W2 to W1? Assume force due to gravity does not change betweenh1 and h2."

I thought this was a simple W = mgh problem, resulting in an answer of 2:1.. but the answer key states its root(2):1! Any idea why?

Related Introductory Physics Homework Help News on Phys.org

#### geosonel

michaelw said:
This is a question from the MCAT, test 3R, and I am stumped as to why the answer is what it is.

"A mass is lifted from the ground to an altitude h1, requiring work W1. The work to lift an identical mass to height h2 is W2. If h2 is twice h1, what is the ratio of W2 to W1? Assume force due to gravity does not change betweenh1 and h2."

I thought this was a simple W = mgh problem, resulting in an answer of 2:1.. but the answer key states its root(2):1! Any idea why?
unless there's more to this problem than you indicated, it appears you're correct that the answer SHOULD be (W2/W1)=2.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving