Question

1. An ideal pendulum has all of its mass m concentrated at the end of a massless string of length L, as shown in the figure. The mass is pulled to a slight angle to the left and released from rest, and it takes exactly 1/8 th of a second to arrive at its maximum position at an equal angle on the right side of equilibrium. What is the frequency f of this motion?

2. An otherwise Earth-like planet is in outer space (without a star to orbit). It has a mass of 5.1×1024 kg. An asteroid which is initially extremely far away (r → ∞) with a speed of 980 m/s is pulled by gravity toward the planet, and orbits in a hyperbolic shape, as shown. At the distance of closest approach (8500 km between their centers), what is the speed of the asteroid?

3. The mass of the Earth is about 6.0 × 1024 kg. What is the speed of a satellite in a circular orbit at a distance of 105 km from the Earth’s center?

Answer 1

See that figure is missing in Question 1 and 2, So add the figures and ask them as a new question. I will be happy to help.

Q3.

Using Force balance on Satellite

Centripetal Force = Gravitational Force

Fc = Fg

m*V^2/R = G*m*Me/R^2

V^2 = G*Me/R

V = sqrt (G*Me/R)

m = mass of satellite

Me = Mass of earth = 6*10^24 kg

G = Gravitational Constant = 6.67*10^-11

R = distance from Earth's center = 10^5 km = 10^8 m

Using these values:

V = Speed of Satellite

V = sqrt (6.67*10^-11*6.0*10^24/10^8)

V = 2000.5 m/sec

Please Upvote.