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1. Can anyone show me how to do this question:
"A length if a cable and the drum it's wrapped around have a combindex mass of 50kg. The mass of the drum is one quarter of the mass of the cable. Removing 35 meters of cable leaves the drum as one third the remaining mass of the cable. Find the original length of the cablr on the drum."
I don't necessarily want you to give me the answer as it'll be more useful to figure the answer out myself but, can someone advise me on how to approach it?
2. (Original post by ChemGeek16)
Can anyone show me how to do this question:
"A length if a cable and the drum it's wrapped around have a combindex mass of 50kg. The mass of the drum is one quarter of the mass of the cable. Removing 35 meters of cable leaves the drum as one third the remaining mass of the cable. Find the original length of the cablr on the drum."
I don't necessarily want you to give me the answer as it'll be more useful to figure the answer out myself but, can someone advise me on how to approach it?
Here's what I'm thinking:

At original length length the mass of the cable is , and at the shorter length the mass is . We can come back to those later.

Considering the masses: (where d is the mass of the drum) and we know that therefore and we can find c, then use this to find d.

Moving onto the second part, we are told and we now know what d is, so we can find C.

Now we know the mass of the drum (d), and the masses of the cable at full (c) and shortened length (C). We need to convert between the length and the mass now. We can say that the length of the cable is proportional to its mass; therefore for the original condition we can say that where L is our original length and we want to find it.

Now, consider and since you know C, the RHS will be in terms of k. You can get the LHS in terms of k by using substitution and you know c. From this point just solve for k and you can find L.
3. (Original post by RDKGames)
Here's what I'm thinking:

At original length length the mass of the cable is , and at the shorter length the mass is . We can come back to those later.

Considering the masses: (where d is the mass of the drum) and we know that therefore and we can find c, then use this to find d.

Moving onto the second part, we are told and we now know what d is, so we can find C.

Now we know the mass of the drum (d), and the masses of the cable at full (c) and shortened length (C). We need to convert between the length and the mass now. We can say that the length of the cable is proportional to its mass; therefore for the original condition we can say that where L is our original length and we want to find it.

Now, consider and since you know C, the RHS will be in terms of k. You can get the LHS in terms of k by using substitution and you know c. From this point just solve for k and you can find L.
Thank you 😊

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