Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

Physics question: Error propagation?

Help! I'm trying to find the error propagation and uncertainty (m ± ∆m) for m where the given formula is

mg = (m1 g sin theta) + (m2 g sin theta)

Note:

m1,m2 = 0.2kg

Theta = 30 degrees

m = unknown value, (though I calculated using the given formula n I got 0.2kg!)

Update:

I'm using 9.8 for g

Relevance
• Anonymous
2 months ago

Update.

mg = m₁gsinθ + m₂gsinθ

The first thing to note is g cancels out giving:

m = m₁sinθ + m₂sinθ

So the value of g isn’t used. I should have spotted that in my first answer.

It is *essential* to know the uncertainties for m₁, m₂ and θ. This will depend on how they have been measured.  But you give no information.  I’ll make up some values for illustration.

There are several different methods and I don’t know which one you are supposed to use.  I’ll show you the simplest method.

m₁ = (0.200±0.001) kg

m₂ = (0.200±0.001) kg

θ = (30±2)º

m = m₁sinθ + m₂sinθ

. . = 0.200* ½ +  0.200* ½

. . = 0.200 kg (agreed)

______________________

m₂_min = 0.199 kg

m₁_max = 0201 kg

m₂_min = 0.199 kg

θ_min  = 28º

θ_max  = 32º

m_min = 0.199sin(28º) + 0.199sin(28º)

. . . . . . .= 0.213kg

m_max = 0.201sin(32º) + 0.201sin(32º)

. . . . . . .= 0.187kg

m = (0.200±0.013) kg