a beam 1.4m long balanced horizontally on a knife edge at its mid point. if a mass of 50g hung at one end of the beam balanced it when the knife edge is placed 0.5m from the same end.calculate the mass of the beam in grams
sum of moments is zero.
50*.5-M(.7-.5)=0
M= 25/.2=125 grams.
To find the mass of the beam, we can utilize the principle of moments. The principle of moments states that the total sum of clockwise moments about a fulcrum point is equal to the total sum of anticlockwise moments about the same point.
In this scenario, the balance point or fulcrum is at the mid-point of the beam. Let's denote the length of the left half of the beam as L and the length of the right half of the beam as L as well. Since the total length of the beam is 1.4m, each half will have a length of L = 1.4m / 2 = 0.7m.
Let's calculate the moments on each side of the beam using the formula: Moment = mass × distance from the fulcrum.
On the left side of the beam, we have:
Moment1 = mass1 × distance1
= 50g × (0.7m - 0.5m)
= 50g × 0.2m
= 10g⋅m
On the right side of the beam, we have:
Moment2 = mass2 × distance2
= mass of the beam × 0.5m
= mass of the beam × (0.7m - 0.2m)
= mass of the beam × 0.5m
According to the principle of moments, the sum of clockwise moments (Moment1) is equal to the sum of anticlockwise moments (Moment2). Thus, we can write the equation:
10g⋅m = mass of the beam × 0.5m
Now, let's solve for the mass of the beam:
mass of the beam = (10g⋅m) / 0.5m
mass of the beam = 20g
Therefore, the mass of the beam is 20 grams.