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mylen
3 months ago
9

You have a set of calipers that can measure thicknesses of a few inches with an uncertainty of 0:005 inches. I mesure the thickn

ess of a deck of 52 cards and get 0.590 in: (a) If you now calculate the thickness of 1 card, what is my answer, including its uncertaintyb) I can improve this result by measuring several decks together. If I want to know the thickness of 1 card with an uncertainty of only 0.00002 inch, how many decks do i need to measure?
Physics
1 answer:
Yuliya22 [3.3K]3 months ago
6 0

To address this issue, we will utilize the principles concerning the calculation of significant figures while considering tolerance levels. Additionally, we must ensure that the total significant digits in the final result does not exceed those of the given values:

PART A) The thickness of the collection of 52 cards is

T = 0.590 \pm 0.005 in

The thickness, t, of a single card can be:

t = \frac{0.590}{52} \pm \frac{0.005}{52} in

t = 0.0113461\pm 0.000096 in

For the 52 cards, the thickness has 3 significant figures and the associated uncertainty has 1 significant digit. Therefore,

the significant figures for one card's thickness and the uncertainty must also align at 3 and 1 respectively.

t = 0.01134 \pm 0.005 in

t = 0.0113 \pm 0.0001 in

Thus, the thickness of an individual card is \mathbf {t = 0.0113 \pm 0.0001 in }

PART B) The uncertainty for one card when measured using a single deck is 0.0001 inch.

The number of decks, n, needed to achieve an uncertainty of 0.00002 inch is

n = \frac{0.0001}{0.00002}

n = 5

Consequently, 5 decks are necessary to measure the thickness of a single card with a 0.00002 inch uncertainty.

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A Honda Civic travels in a straight line along a road. The car’s distance x from a stop sign is given as a function of time t by
serg [3582]

a) Average velocity: 2.8 m/s

b) Average velocity: 5.2 m/s

c) Average velocity: 7.6 m/s

Explanation:

a)

The car's position over time t can be described by

x(t)=\alpha t^2 - \beta t^3

where

\alpha = 1.50 m/s^2

\beta = 0.05 m/s^3

To find the average velocity, we divide the displacement by the elapsed time:

v=\frac{\Delta x}{\Delta t}

At time t = 0, the position is:

x(0)=\alpha \cdot 0^2 - \beta \cdot 0^3 = 0

At time t = 2.00 s, the position is:

x(2)=\alpha \cdot 2^2 - \beta \cdot 2^3=5.6 m

This leads us to the displacement of

\Delta x = x(2)-x(0)=5.6-0=5.6 m

The duration for this interval is

\Delta t = 2.0 s - 0 s = 2.0 s

Therefore, the average velocity during this period is

v=\frac{5.6 m}{2.0 s}=2.8 m/s

b)

At time t = 0, the position is:

x(0)=\alpha \cdot 0^2 - \beta \cdot 0^3 = 0

At time t = 4.00 s, the position is:

x(4)=\alpha \cdot 4^2 - \beta \cdot 4^3=20.8 m

Thus, the displacement is

\Delta x = x(4)-x(0)=20.8-0=20.8 m

The time interval is

\Delta t = 4.0 - 0 = 4.0 s

This yields an average velocity of

v=\frac{20.8}{4.0}=5.2 m/s

c)

The position at t = 2 s is:

x(2)=\alpha \cdot 2^2 - \beta \cdot 2^3=5.6 m

And at t = 4 s it is:

x(4)=\alpha \cdot 4^2 - \beta \cdot 4^3=20.8 m

This gives us a displacement of

\Delta x = 20.8 - 5.6 = 15.2 m

While the time interval is

\Delta t = 4.0 - 2.0 = 2.0 s

So the resulting average velocity is

v=\frac{15.2}{2.0}=7.6 m/s

Find out more about average velocity:

6 0
3 months ago
Write a hypothesis about the effect of increasing voltage on the current in the circuit. Use the "if . . . then . . . because .
Yuliya22 [3333]

Hypothesis: An increase in voltage should result in a corresponding rise in current because according to Ohm's Law,

I \propto V

I=\frac{V}{R}

Ohm's Law indicates that current is proportional to voltage when resistance remains constant. Hence, if resistance stays the same, elevating the voltage will lead to an increase in current. Conversely, if voltage remains unchanged and resistance increases, current will decrease.

3 0
3 months ago
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A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete
Sav [3153]

Answer:

407 steps

Explanation:

Based on the question,

P = mgh/t........... Equation 1

Where P stands for power, m is mass, g denotes gravity, h is height, and t represents time.

Rearranging the equation to solve for h, we have:

h = Pt/mg............. Equation 2

Providing values: P = 746 W, t = 1 minute = 60 seconds, m = 70 kg.

Given constant: g = 9.8 m/s²

By substituting into equation 2

h = 746(60)/(70×9.8)

h = 44760/686

h = 65.25 m

h = 6525 cm

Calculating number of steps: 6525/16

The resulting number of steps = 407 steps

6 0
3 months ago
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