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Answer:
44.6 N
Explanation:
Draw a free body diagram of the block. There are four forces on the block:
Weight force mg pulling down,
Normal force N pushing up,
Friction force Nμ pushing left,
and applied force F pulling right 30° above horizontal.
Sum of forces in the y direction:
∑F = ma
N + F sin 30° − mg = 0
N = mg − F sin 30°
Sum of forces in the x direction:
∑F = ma
F cos 30° − Nμ = 0
F cos 30° = Nμ
N = F cos 30° / μ
Substitute:
mg − F sin 30° = F cos 30° / μ
mg = F sin 30° + (F cos 30° / μ)
Plug in values:
mg = 20 N sin 30° + (20 N cos 30° / 0.5)
mg = 44.6 N
Answer:
a) x = (0.0114 ± 0.0001) in
, b) the number of decks is 5
Explanation:
a) The thickness of the deck of cards (d) is measured and the thickness of a card (x) is calculated
x = d / 52
x = 0.590 / 52
x = 0.011346 in
Let's look for uncertainty
Δx = dx /dd Δd
Δx = 1/52 Δd
Δx = 1/52 0.005
Δx = 0.0001 in
The result of the calculation is
x = (0.0114 ± 0.0001) in
b) You want to reduce the error to Δx = 0.00002, the number of cards to be measured is
#_cards = n 52
The formula for thickness is
x = d / n 52
Uncertainty
Δx = 1 / n 52 Δd
n = 1/52 Δd / Δx
n = 1/52 0.005 / 0.00002
n = 4.8
Since the number of decks must be an integer the number of decks is 5
