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Alla [95]
3 years ago
8

You have a set of calipers that can measure thicknesses of a few inches with an uncertainty of ± 0.005 inches. You measure the t

hickness of a deck of 52 cards and get 0.590 in:a. If you now calculate the thickness of 1 card, what is your answer, including its uncertainty?b. You can improve this result by measuring several decks together. If you want to know the thickness of 1 card with an uncertainty of only 0.00002 in., how many decks do you need to measure together?
Physics
1 answer:
Bond [772]3 years ago
3 0

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

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A girl drops a stone from the top a tower 45m tall. At the same time, a boy standing at the base of the tower, projects another
Advocard [28]

Answer:

(i) The stones meet at 1.8 second

(ii) The point at which the stones meet, is 28.8 m above the base of the building and 16.2 m below the top of the building.

Explanation:

(i)

First we consider the stone dropped by the girl. We have data:

Vi = Initial Velocity of Stone = 0 m/s   (Since the stone was initially at rest)

t = Time Period

g = 10 m/s²

s₁ = Distance Covered by Stone

Using 2nd equation of motion, we get:

s₁ = Vi t + (0.5)gt²

s₁ = (0)(t) + (0.5)(10)t²

s₁ = 5t²   ----- equation (1)

Now, we consider the stone throne vertically upward by the boy. We have data:

Vi = Initial Velocity of Stone = 25 m/s

t = Time Period

g = - 10 m/s²   (negative sign due to upward motion)

s₂ = Distance Covered by Stone

Using 2nd equation of motion, we get:

s₂ = Vi t + (0.5)gt²

s₂ = (25)(t) + (0.5)(-10)t²

s₂ = 25t - 5t²   ----- equation (2)

At, the point where both the stones meet, the sum of distances covered by both stones must be equal to the height of building (i.e 45 m).

s₁ + s₂ = 45

using values from equation (1) and equation (2)

5t² + 25t - 5t² = 45

25t = 45

t = 45/25

<u>t =  1.8 sec</u>

(ii)

using this value of of t in equation (2)

s₂ = (25)(1.8) - (5)(1.8)²

<u>s₂ = 28.8 m</u>

using this value of of t in equation (1)

s₁ = (5)(1.8)²

<u>s₁ = 16.2 m</u>

<u>Hence, the point at which the stones meet, is 28.8 m above the base of the building and 16.2 m below the top of the building.</u>

6 0
3 years ago
What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29.5 km/h and the μs
Yakvenalex [24]

Answer:

Radius=15.773 m

Explanation:

Given data

v=29.5 km/h=8.2 m/s

μs=0.435

To find

Radius R

Solution

The acceleration is a centripetal acceleration  which is experienced by the bicycle given by

a=v^{2}/R

This acceleration is only due to static force which given as

f=ma\\f=m(v^{2}/R )

The maximum value of the static force is given as

Fs_{max}=u_{s}F_{N}

where

FN is normal force equal to mass*gravity

Therefore when the car is on the verge of sliding

f=fs_{max}\\ m(v^{2}/R )=u_{s}mg

Therefore the minimum radius should be found by the bicycle move without  sliding

So

v^{2}/R=u_{s}g\\  R=v^{2}/u_{s}g\\R=(8.2)^{2}/(0.435*9.8)\\R=15.773m

8 0
3 years ago
Hi i need help. thNKS
Ede4ka [16]

Answer:

8

Explanation:

Groups go down, periods go across :)

3 0
3 years ago
For the strongest electromagnet, what wire gauge should be used?
alexandr1967 [171]

Answer:

Thick

Explanation:

Thicker wure enables higher AMP's, assuming your supply is capable, so indirectly thicker wire may help. Thicker wire takes up more space. So does more turns.

Hope this helped. Have a blessed day !

7 0
2 years ago
In addition to light and chlorophyll photosynthesis requires
labwork [276]

Answer:

Water (H₂O) and Carbon dioxide (CO₂)

Explanation:

Photosynthesis usually refers to the process by which the green plants can synthesize their own food in the presence of sunlight, water, carbon dioxide, and light. This process helps in the conversion of light energy into chemical energy.

In addition to the sunlight and chlorophyll, the process of photosynthesis requires water as well as carbon dioxide. The plants are comprised of green pigments on their leaves that are commonly known as chlorophyll. These pigments absorb the water molecules and carbon dioxide gas that helps in synthesizing their food.

The equation for the process of photosynthesis is given below:

6CO₂ + 6H₂0 + (energy) → C₆H₁₂O₆ + 6O₂

6 0
3 years ago
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