Calculate the length of a wooden beam that is 50cm. 2. Given that a piece of woo

Question

Calculate the length of a wooden beam that is 50cm.

2. Given that a piece of wood 1.75cm x 3.6cm x 20cm has a mass of 64.5 grams, calculate the mass of a wooden beam that has the same cross section with length 50cm.

3. Add 47.5g to the total mass of the components from Tool Training Homework 1 (66.5g) to find the mass of your counter balance assembly.

4. Find the balance point of your beam and counter balance assembly using the formula:

(beam mass)(beam length/2) = (distance to balance point)(total mass of beam and counterbalance)

Example: Amy’s beam is 560mm long and has a mass of 180.6g, while her counter balance assembly has a mass 145g. (180.6)(560/2) = (X)(180.6+145) 50568=(X)(325.6) X=155.3 So, the balance point of Amy’s beam and the counter balance assembly is 155.3mm from the end where the counter balance assembly will be mounted.

Explanation / Answer

>> Part (2).

>> As, mass = Volume X Density

and, Volume = Area X Length

>> Now, as density of area of cross section is same

=> mass / Length = Constant

=> m1/L1 = m2/L2

=> m2 = (64.5)*(50/75) = 43 g

=> Mass of Wooden Beam = 43 g

>> Part (3).

>> As, Total mass of the components from Tool Training Homework = 66.5g

=> Mc = mass of counter balance assembly = 66.5 + 47.5 = 114 g

>> Part (4).

>> As, (beam mass)(beam length/2) = (distance to balance point)(total mass of beam and counterbalance)

>> Now, putting all values here,

=> 43*50 = Y*(66.5+114)

=> Y = Distance to balance point = 11.91 cm ....ANSWER...

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