An instrument to measure the acceleration of gravity on Mars is constructed of a spring from which is suspended a mass of 0.40 kg. At a place on earth where the local acceleration of gravity is 9.81 ms?, the spring extends 1.08 cm. When the instrument package is landed on Mars, it radios the information that the spring is extended 0.40 cm. What is the Martian acceleration of gravity?.

3) pull the ball to the side until the string makes an angle of 35.0° degrees with the vertical and release it from rest. At the bottom of the swing, the ball is moving at 2.25 m/s. You build a simple pendulum from a ball attached to the end of a very light string. You How long is the string?

a) Find the surface gravity and escape velocity of a planet with a mass of (6.7× 1023 kg) and a radius of (2.9 × 106 m).b) What is the local acceleration due to gravity of a planet on which a pendulum of length (0.4 m) undergoes (5 oscillations) in (13 s)?c) If the planet from part (b) has a radius of (R = 5 × 106 m), what is the mass of the planet?

5.)  Imagine a 5.00 kg mass hanging from a rope on a planet with a value of g=0.500 m/s^2.  In addition, there is a spring that goes straight down from the mass to the ground, and the spring has a spring constant of k=20 N/m. The spring has been stretched from its equilibrium position by 4.00 cm.  The rope will break if the tension exceeds 5 N. (5a) Draw a free-body diagram for the mass, labeling all forces. (5b) What is the tension in the rope? (5c) The mass is slowly lifted using the rope, so that the spring continues to stretch.  How many more centimeters can you stretch the spring before the rope breaks?

A mass mm is suspended from a massless spring of natural length 90 cm with the spring constant k=10 Nm-1 and causes the spring to extend by 8.6 cm.  Assuming the gravitational field strength g=9.8g, calculate the value of the mass on the spring.

An astronaut lands on a foreign world and wants to measure the local gravitational field strength where he lands. He takes a 0.31m length pendulum and holds it 4 degrees from the vertical. He then releases the pendulum and measures that it takes 7.85 seconds for the pendulum to swing through 10 cycles of swing. What is the gravitational field strength on the planet?

A mass of 0.12 kg is sliding on a frictionless horizontal surface when it comes to a horizontal spring with Hooke’s constant k = 90 N/m. The mass is moving at 15 m/s. How far does the spring compress? What is the acceleration of the mass when the spring is fully compressed? How much time elapses between when the mass first encounters the spring, and when the spring reaches full compression? a.) Set up and solve for maximum compression distance. b.) Set up and solve for acceleration at maximum compression. c.) Set up and solve for the time to maximum compression.

Asimple pendulum which has a frequency of 2.5 Hz.on the surface of the Earth is used by an astronaut visiting a newly discovered planet. On that planet's surface, the pendulum swings with a frequency of 1.6 Hz. How large is the gravitational acceleration of that planet?