The Physics of Everyday Phenomena
The Physics of Everyday Phenomena
8th Edition
ISBN: 9780073513904
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
Question
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Chapter 21, Problem 1SP

(a)

To determine

The number of seconds in a year.

(a)

Expert Solution
Check Mark

Answer to Problem 1SP

The number of seconds in a year is 3.15×107s.

Explanation of Solution

One year has 365days, one day has 24h, 1h has 60min and 1min has 60s. The number of seconds in a year is obtained as,

Number of seconds in 1y=(1y)(365days1y)(24h1day)(60min1h)(60s1min)=3.15×107s

Conclusion:

Therefore, the number of seconds in a year is 3.15×107s.

(b)

To determine

The number of meters in 1ly.

(b)

Expert Solution
Check Mark

Answer to Problem 1SP

The number of meters in 1ly is 9.46×1015m.

Explanation of Solution

One light-year (1ly) is the distance travelled by light ray in one year. The light travels with a speed of 3×108m/s through vacuum. So, the number of meters in 1ly is the distance travelled by the light ray in meters, during the time of 1y.

Write the expression for the distance travelled by the light ray in a given time.

d=ct

Here,

d is the distance travelled by light ray

c is the speed of light

t is the time

Substitute 3×108m/s for c and 1y for t to find d.

d=(3×108m/s)(1y)=(3×108m/s)(1y×365days1y×24h1day×60min1h×60s1min)=9.46×1015m

Since there distance travelled by light ray in one year is obtained as 9.46×1015m, the number of meters in 1ly is equal to the same.

Conclusion:

Therefore, the number of meters in 1ly is 9.46×1015m.

(c)

To determine

The distance to the nearest star to the sun in meters.

(c)

Expert Solution
Check Mark

Answer to Problem 1SP

The distance to the nearest star to the sun in meters is 3.78×1016m.

Explanation of Solution

Given info: The distance to the nearest star to sun is about 4ly.

The distance in meters, equivalent to one light-year is 9.46×1015m. Therefore, the distance (d) equivalent to 4ly is obtained as,

d=4(9.46×1015m)=3.78×1016m

Hence, the distance between the sun and the nearest star is 3.78×1016m.

Conclusion:

Therefore, the distance to the nearest star to the sun in meters is 3.78×1016m.

(d)

To determine

The time taken to reach the nearest star if one travels with the speed one-tenth of the speed of light.

(d)

Expert Solution
Check Mark

Answer to Problem 1SP

The time taken to reach the nearest star if one travels with the speed one-tenth of the speed of light is 40y.

Explanation of Solution

Given info: The distance between the sun and the nearest star is 3.78×1016m and the speed of the traveler is c/10.

Write the expression for the time of travel in terms of distance and speed.

t=dv

Here,

t is the time of travel

d is the distance

v is the speed

Substitute 3.78×1016m for d and c/10 for v with c=3×108m/s to find the time taken to reach the nearest star if one travels with the speed one-tenth of the speed of light.

t=3.78×1016m(c10)=3.78×1016m(3×108m/s10)=1.26×109s×1h3600s×1day24h×1y365days=40y

Conclusion:

Therefore, the time taken to reach the nearest star if one travels with the speed one-tenth of the speed of light is 40y.

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