1. a) An apple weighs 1.12 N . When you hang it from the end of...

Free

50.1K

Verified Solution

Question

Physics

1.
a) An apple weighs 1.12 N . When you hang it from the end of along spring of force constant 1.57 N/m and negligible mass, itbounces up and down in SHM. If you stop the bouncing and let theapple swing from side to side through a small angle, the frequencyof this simple pendulum is half the bounce frequency. (Because theangle is small, the back and forth swings do not cause anyappreciable change in the length of the spring.)
What is the unstretched length of the spring (i.e., without theapple attached)?
b) On the planet Newtonia, a simple pendulum having a bob withmass 1.50 kg and a length of 165.0 cm takes 1.36 s , when releasedfrom rest, to swing through an angle of 12.5 _?, where itagain has zero speed. The circumference of Newtonia is measured tobe 51400 km.
What is the mass of the planet Newtonia?

Answer & Explanation Solved by verified expert

4.1 Ratings (775 Votes)

Q1.

part a:

frequency in SHM with the spring in vertical direction=(1/(2*pi))*sqrt(k/m)

where k=spring constant=1.57 N/m

m=mass =weight/g=1.12/9.8=0.58989 Hz

when it is swinging from side to side,

frequency=(1/(2*pi))*sqrt(g/L)

given this frequency is half of the bounce frequency

hence (1/(2*pi))*sqrt(g/L)=0.58989

==>sqrt(9.8/L)=3.7064

==>L=0.71338 m

part b:

let radius be r and and mass of the planet be M.

circumference=51400 km=5.14*10^7 m

==>2*pi*r=5.14*10^7

==>r=8.1806*10^6 m

for the pendulum:

time taken to reach from rest to the max angle where it is again at rest is (1/4)th of the time period

hence 1/4*time period=1.36

==>time period=5.44 seconds

as for. a simple pendulum, time period=2*pi*sqrt(L/g)

==>2*pi*sqrt(1.65/g)=5.44

==>g=2.2011 m/s^2

as g for any planet is given as G*M/r^2

==>6.674*10^(-11)*M/(8.1806*10^6)^2=2.2011

==>M=2.2011*(8.1806*10^6)^2/(6.674*10^(-11))

==>M=2.2071*10^24 kg

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member