a fis is suspended from a 6m uniform beam supported by a cable and attached by a pivot to the ground. the beam has a mass of 20 kg and the cable can withstand a maximum tension of 10000 N. find masimum wright of a fish that can be supported by this system
To find the maximum weight of the fish that can be supported by this system, we need to consider the forces acting on the beam and determine the maximum tension in the cable before it reaches its capacity.
Let's break down the forces acting on the system:
1. Weight of the beam: The beam has a mass of 20 kg and is subject to the force of gravity. The weight can be calculated using the formula: weight = mass x acceleration due to gravity = 20 kg x 9.8 m/s² = 196 N.
2. Cable tension: The cable supports the beam and the fish, and it experiences tension. To determine the maximum tension, we need to consider the maximum possible weight that the system can support.
3. Weight of the fish: Let's assume the weight of the fish is represented by W.
Considering the equilibrium of the system, the sum of the forces acting vertically should be zero. Therefore:
Tension in the cable + Weight of the beam + Weight of the fish = 0
T + 196 N + W = 0
Now we can find the maximum weight (W) that the system can support by determining the maximum tension (T) that the cable can withstand.
According to the given information, the cable can withstand a maximum tension of 10000 N. So, we have:
T ≤ 10000 N
Substituting the value of T in the equation above:
10000 N + 196 N + W = 0
Simplifying the equation:
W = -10000 N - 196 N
W = -10196 N
Since weight cannot be negative, it means that the system cannot support any weight greater than 10196 N. Therefore, the maximum weight of the fish that can be supported by this system is 10196 N.