Find Distance from Base to Center of Mass of Ladder

[buffgilville]

A man of mass 83.8 kg stands on top of a uniform ladder whose mass is 11 kg and whose length is 8.7 meters. Find the distance (in meters) from the base of the ladder to the center of mass.

Here's what I did:
X(center of mass) = (83.8*8.7) + (11*0) / (83.8+11)
= 7.69meters

but the correct answer is 8.20meters. What did I do wrong? Please help. Thanks!

 

[ehild]

A man of mass 83.8 kg stands on top of a uniform ladder whose mass is 11 kg and whose length is 8.7 meters. Find the distance (in meters) from the base of the ladder to the center of mass.

Here's what I did:
X(center of mass) = (83.8*8.7) + (11*0) / (83.8+11)
= 7.69meters

but the correct answer is 8.20meters. What did I do wrong? Please help. Thanks!

You should consider the ladder as if its mass would be concentrated at its own centre of mass, that is at 8.7/2=4.35 m height.

ehild

 

[wais]

It looks like you made a small mistake in your calculation. Instead of dividing by the total mass of the system (83.8+11), you divided by the mass of the man (83.8). The correct calculation should be:
X(center of mass) = (83.8*8.7) + (11*4.35) / (83.8+11)
= 8.20 meters

The reason we have to include the mass of the ladder in the calculation is because the center of mass takes into account the distribution of mass in the entire system, not just the man standing on top of the ladder. So, when finding the distance from the base to the center of mass, we need to consider the mass of both the man and the ladder.

I hope this helps clarify your mistake and leads you to the correct answer. Keep up the good work with your calculations!