A 320 N bench is 2.40m long. The legs are .30m from each end and weigh 15.0 N each. If 3 persons weighing in order ,500 N, 750N, and 1000N sit .40m, 1.20m, and 2m respectively from one end of the bench, what downward force must each set of legs exert on the floor?
weight = 320+ 4*15 + 500 + 750 + 1000 = total force up
moments around one end
Ff=force up from floor at far end
Fn = force up at near end
320(1.2)-Fn*.3+30*.3+500*.4+750*1.2
+1000*2 +30*2.1-Ff*2.1 = 0
but Fn = (total force up - Ff)
To find the downward force that each set of legs must exert on the floor, we need to consider the forces acting on the bench. Let's break down the problem step by step:
Step 1: Calculate the total weight of the bench legs.
The bench has two legs, each weighing 15.0 N. Therefore, the total weight of the bench legs is 2 * 15.0 N = 30.0 N.
Step 2: Calculate the total weight applied by the people sitting on the bench.
The first person weighs 500 N and sits 0.40 m from one end of the bench.
The second person weighs 750 N and sits 1.20 m from one end of the bench.
The third person weighs 1000 N and sits 2.00 m from one end of the bench.
To calculate the applied weight of each person, we multiply their weight by the acceleration due to gravity (9.8 m/s^2) and the distance from their position to the end of the bench.
Weight applied by the first person = 500 N * 9.8 m/s^2 * 0.40 m = 196 N
Weight applied by the second person = 750 N * 9.8 m/s^2 * 1.20 m = 882 N
Weight applied by the third person = 1000 N * 9.8 m/s^2 * 2.00 m = 19,600 N
The total weight applied by all three people is the sum of their individual weights:
Total weight applied by all three people = 196 N + 882 N + 19,600 N = 20,678 N
Step 3: Calculate the weight of the bench itself.
The bench weighs 320 N.
Step 4: Calculate the resulting downward force on each set of legs.
To find the downward force on each set of legs, we add up the weight of the bench, the weight of the bench legs, and the total weight applied by the people.
For the legs at one end of the bench (where the third person is sitting):
Downward force on the legs = Weight of bench + Weight of bench legs + Total weight applied by people
Downward force on the legs = 320 N + 30 N + 20,678 N = 21,028 N
For the legs at the other end of the bench (where nobody is sitting):
Downward force on the legs = Weight of bench + Weight of bench legs
Downward force on the legs = 320 N + 30 N = 350 N
Therefore, the downward force that each set of legs must exert on the floor is 21,028 N for the legs where the third person is sitting and 350 N for the legs where nobody is sitting.