"To buy a bed with" vs "to play a ball with"

I got into a discussion with a friend and we're trying to figure out why we omit with when we say

I have no money to buy a bed [with]

when, grammatically, it's the same as

I have no ball to play soccer with.

In this case, having with is correct, while in the case of the first sentence, it feels weird to have with at the end of the sentence.

Also,

I have no time to study.

I have no one to study with.

Again, how would I explain why we omitted with in the first sentence? I understand why we need it in the second one though.

I suspect that when we depart from the resource/object during the act, we feel weird to use "with". In your examples, we depart from money and time; while we do not depart from ball and "one".

Because you don't really say:

I buy a bed with money.

I play soccer with a ball.

I study with time.

Do something with something, can have two meanings:

• I cooked my meal with a microwave oven
• I cooked my meal with my friends

It is not weird because you are adding extra information to your action (cooking). A meal can be cooked by a steamer, or cooked alone. By saying "with a microwave oven" or "with friends", you are adding extra information to describe what were you doing.

However, saying "buy something with money" is weird because it does NOT, contextually, add any meaningful information, to better describe what were you doing. Saying "I buy a bed with my credit card." would not feel weird.

If I say:

I walk to get over there.

I hear your voice to listen to you speak.

The temperature of the cold water is very low.

It would be weird, too. It is describing something you already described.