Ten bags of top soil, each weighing 150 N, are placed on a L = 2.95 m long sheet of wood. They are stacked 0.50 m from one end of the sheet of wood, as shown in Figure 8-27. Two people lift the sheet of wood, one at each end. Ignore the weight of the wood, how much force must each person exert?

To find out how much force each person must exert, we need to consider the distribution of weight along the sheet of wood.

First, let's calculate the total weight of the ten bags of top soil. Each bag weighs 150 N, and there are ten bags, so the total weight is:

Total weight = 150 N/bag × 10 bags = 1500 N

Next, we need to determine the center of mass of the system. Since the bags are stacked 0.50 m from one end, the center of mass is located at:

Center of mass = 2.95 m - 0.50 m = 2.45 m from one end

To simplify the problem, we can consider the system as two equal halves. Each person will lift one half of the weight.

Since the center of mass is at 2.45 m, the distance from each person to the center of mass is half of the length of the sheet of wood:

Distance from person to center of mass = 2.45 m / 2 = 1.225 m

To calculate the force required for each person, we can use the principle of torque. The torque exerted by the weight on each end is balanced by the torque exerted by the force applied by the person. We can express this as an equation:

Torque from weight = Torque from force

The torque exerted by the weight on each end is the product of the weight and the distance from the center of mass:

Torque from weight = Weight × Distance from person to center of mass

The torque exerted by the force applied by the person is the product of the force and the length of the sheet of wood:

Torque from force = Force × Length of sheet of wood

Now, let's plug in the values we know:

Torque from weight = 1500 N × 1.225 m

Torque from force = Force × 2.95 m

Setting the two torques equal to each other:

1500 N × 1.225 m = Force × 2.95 m

Now, we can solve for the force required for each person:

Force = (1500 N × 1.225 m) / 2.95 m

Force ≈ 618.644 N

Each person must exert approximately 618.644 N of force to lift the sheet of wood with the ten bags of top soil.

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