The mass of the sign shown is 28.5 kg. Find the weight supported by (a) the left support and (b) the right support.

Between the left and right support is 0.900m and from the right support to the end of the sign is 0.300m.

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| | --------> (0.900m)|| --->(0.300m)

I got answers: a. 111.1 and b. 186.2 but I'm not sure if they're correct. Can someone please help?

Weight of the sign is W = mg = 28.5kg•9.8m/s² = 297.3N

The sum the moments around the left bottom of the sign.
Clockwise moment Mcw = 297.3N • (1.2m/2) = 167.6 N•m
Counterclockwise moment Mccw = F•0.9m
That is, the cw rotation of the sign about the left corner is resisted by a support force.
F = 167.6N•m / 0.9m = 186.2N ← in the right column

The left support can be determined in a similar fashion, or simply by noting that it must support the remaining vertical force:
Left F = W - Fr = 297.3N - 186.2N = 111.1N ← left support

28.5x9.80 = 279.3 not 297.3.

therefore the left support would equal 93.1 not 11.1

To find the weight supported by each support, we first need to understand the concept of weight and how it relates to mass and gravity.

Weight is the force with which an object is pulled towards the center of the Earth due to gravity. It is calculated using the formula:

Weight = mass x acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s² on the surface of the Earth.

Now, let's calculate the weight supported by each support.

(a) Left Support:

Since the mass of the sign is given as 28.5 kg, we can calculate the weight supported by the left support using the formula:

Weight supported by the left support = mass x acceleration due to gravity

Weight supported by the left support = 28.5 kg x 9.8 m/s²

Weight supported by the left support = 279.3 N

Therefore, the weight supported by the left support is 279.3 Newtons.

(b) Right Support:

To find the weight supported by the right support, we need to consider the distribution of weight along the length of the sign.

From the given dimensions, we know that the distance between the left and right supports is 0.900 m, and from the right support to the end of the sign is 0.300 m.

The weight supported by the right support will be greater than the weight supported by the left support due to the longer lever arm (0.900 m vs. 0.300 m).

To find the weight supported by the right support, we can use the concept of torque.

Torque = Force x Lever Arm

The torque on the right support will be equal to the torque on the left support because the sign is in equilibrium.

Therefore, the weight supported by the right support can be calculated as follows:

Weight supported by the right support = (Weight supported by the left support x Lever Arm of left support) / Lever Arm of right support

Weight supported by the right support = (279.3 N x 0.900 m) / 0.300 m

Weight supported by the right support = 837.9 N

Therefore, the weight supported by the right support is 837.9 Newtons.

So, the correct answers are:

(a) The weight supported by the left support is 279.3 Newtons.
(b) The weight supported by the right support is 837.9 Newtons.