What is the smallest number of whole logs (ñ = 725 kg/m3, radius = 0.0800 m, length = 3.60 m) that can be used to build a raft that will carry four people, each of whom has a mass of 60.0 kg?
I do not know how to start this.
20 logs
To determine the smallest number of whole logs required to build a raft that can carry four people, you need to calculate the total weight of both the logs and the people.
Here's how you can do it step by step:
1. Calculate the weight of each log:
- The density (ñ) of the log is given as 725 kg/m3.
- The radius (r) of the log is given as 0.0800 m, so the cross-sectional area (A) of each log can be calculated using the formula: A = π * r^2.
- The length (L) of each log is given as 3.60 m.
- The volume of each log (V) can be calculated using the formula: V = A * L.
- Finally, the weight of each log (Wlog) can be calculated using the formula: Wlog = ñ * V.
2. Calculate the total weight of the logs:
- Since the number of logs required is not known initially, you can denote it as 'n'.
- The total weight of the logs (Wtotal_logs) can be calculated by multiplying the weight of each log (Wlog) by the number of logs (n).
3. Calculate the total weight of the people:
- Since there are four people and each person has a mass of 60.0 kg, the total weight of the people (Wtotal_people) can be calculated by multiplying the mass of each person (60.0 kg) by the number of people (4).
4. Determine the number of logs required:
- The number of logs required (n) can be determined by dividing the total weight of the people (Wtotal_people) by the weight of each log (Wlog). Round up to the nearest whole number since you can't have a fraction of a log.
By following these steps, you can find the smallest number of whole logs needed to build the raft that can carry four people with the given specifications.