College Physics Problem 1.11


Suppose that your bathroom scale reads your mass as 65 kg with a 3%  uncertainty. What is the uncertainty in your mass (in kilograms)?


Solution:

The uncertainty is computed as 

\displaystyle \delta _m=\frac{3\:\%}{100\:\%}\times 65\:kg=1.95\:kg           ☚

Therefore, the uncertainty in the given mass is 1.95 kg.


College Physics Problem 1.10


a) The average distance between the Earth and the Sun is  108 km. Calculate the average speed of the Earth in its orbit in kilometers per second. 

b) What is this is meters per second?


Continue reading “College Physics Problem 1.10”

College Physics Problem 1.9


Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year.
(a) What distance does it move in 1.0 s at this speed?
(b) What is its speed in kilometers per million years?


Solution:

Part a

We know that the formula for the distance traveled, d, if we are given rate, r, and time, t is given by \displaystyle d=r\times t

Therefore, the distance traveled is 

\displaystyle d=\left(4\:\frac{cm}{year}\times \frac{1\:year}{365\:\frac{1}{4}\:days}\times \frac{1\:day}{24\:hours}\times \frac{1\:hour}{60\:mins}\times \frac{1\:min}{60\:s}\right)\left(1\:s\right)

\displaystyle d=1.3\times 10^{-7}\:cm\:

\displaystyle d=1.3\times 10^{-9}\:m

Therefore, the distance traveled by the tectonic plate is about \displaystyle 1.3\times 10^{-9}\:m          ☚

Part b

We need to convert 4.0 cm/year to km/My. 

\displaystyle 4.0\:\frac{cm}{year}\times \frac{1\:m}{100\:cm}\times \frac{1\:km}{1000\:m}\times \frac{1\:000\:000\:years}{1\:My}=40\:\frac{km}{My}

Therefore, the speed of the tectonic plates is 40 km/My.          ☚


College Physics Problem 1.2.8


The speed of sound is measured to be  342 m/s on a certain day. What is this in km/h?


Solution:

We know that 1 km=1000 m and 1 hr=3600 sec.

Convert 342 m/s.

\displaystyle 342\:m/s=\left(342\:\frac{m}{s}\right)\left(\frac{1\:km}{1000\:m}\right)\left(\frac{3600\:s}{1\:hr}\right)=1231.2\:km/hr          ☚

Therefore, the speed of sound in km/hr is 1231.2 km/hr.


College Physics Problem 1.2.7


Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)


Solution:

Convert 29028 ft to km

\displaystyle 29,028\:ft=\left(29\:028\:ft\right)\left(\frac{1\:km}{3281\:ft}\right)=8.847\:km          ☚

Therefore, the height of Mount Everest is 8.847 kilometers.


College Physics Problem 1.2.2


A car is traveling at a speed of 33 m/s .
(a) What is its speed in kilometers per hour?
(b) Is it exceeding the 90 km/h speed limit?


Solution:

Part a

\displaystyle 33\:m/s=\left(33\:\frac{m}{s}\right)\left(\frac{1\:km}{1000\:m}\right)\left(\frac{3600\:s}{1\:hr}\right)=118.8\:km/hr

Part b

At 118.8 km/h, the car is traveling faster than the speed limit.