a bench is 2.4m long.the legs are attached .3m from each end.if 3 boys weighing 500n,750n,1000n seated.4,1.2m,2m from end of the bench,what force must eachset of leg exert
To determine the force that each set of legs must exert, we need to consider the weight distribution of the boys on the bench. Let's calculate the forces exerted by each set of legs step by step.
1. Find the total weight on the bench:
- Boy 1 weighs 500N.
- Boy 2 weighs 750N.
- Boy 3 weighs 1000N.
So, the total weight on the bench is 500N + 750N + 1000N = 2250N.
2. Calculate the weight distribution between the two sets of legs:
- The weight of the bench itself is distributed equally on both ends, so each set of legs supports half of the bench's weight.
- The boys create additional weight distribution based on their positions.
Let's break it down:
- Boy 1 is seated 4m from one end, so his weight is evenly distributed to both sets of legs.
- Boy 2 is seated 1.2m from one end, meaning 2.4m - 1.2m = 1.2m is the distance between Boy 2 and the other end. Thus, 1.2m of the bench's weight is supported by the legs on the same side.
- Boy 3 is seated 2m from one end, meaning 2.4m - 2m = 0.4m is the distance between Boy 3 and the other end. Therefore, 0.4m of the bench's weight is supported by the legs on the same side.
3. Calculate the forces exerted by each set of legs:
- We'll denote the force exerted by the legs closest to Boy 1 as "F1" and the force exerted by the other set of legs as "F2".
- F1 supports half the weight of the bench (since Boy 1 is sitting in the middle) and the weight distribution caused by Boy 2. Thus, F1 = (2250N/2) + (750N * 1.2m / 2.4m).
- F2 also supports half the weight of the bench (since Boy 1 is sitting in the middle) and the weight distribution caused by Boy 3. Thus, F2 = (2250N/2) + (1000N * 0.4m / 2.4m).
Now, you can substitute the given values into the equations to find the exact forces exerted by each set of legs.