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Simple Harmonic Motion: Pendulum

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Wize University Physics Textbook (Master) > Periodic Motion: Oscillations

Basic Concepts of Oscillation

4 Activities

Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Gravitational Force

4 Activities

You have landed on an unknown planet. You have a simple pendulum with a length of 25.0 cm25.0\ cm. You measure the frequency of oscillation of the pendulum to be 0.5 Hz0.5\ Hz.

a) What is the gravitational acceleration on this planet? (in m/s^2)
b) What would be the period of the oscillation if you used this pendulum on Earth? (in seconds)
More Basic Concepts of Oscillation Questions:
Practice: Spring and mass system
A block of unknown mass mmis attached to a horizontal spring which has a spring constant k=4.8 Nmk=4.8\ \frac{N}{m}. It is then set oscillating on a frictionless surface with an amplitude A=12 cmA=12\ cm. The position and velocity of the block at t=0t=0are measured to be +6.0 cm+6.0\ cmand +30 cms+30\ \frac{cm}{s}, respectively.
The motion can be modeled as an equation in the form x(t)=Acos⁡(ωt+φ)x\left(t\right)=A\cos\left(\omega t+\varphi\right).
Simple harmonic motion: Pendulum
In two separate experiments a pendulum and a mass-spring are moved from the Earth to the moon surface where gravitational acceleration is 16\frac{1}{6}of the Earth.
a) How does the amplitude of oscillations change for each system?
b) How does the frequency of oscillations change for each system?
The displacement function of a simple harmonic motion over time is shown below. Write the equation of the motion.
A mass is on a spring. The spring is stretched and then released so that the mass bounces back and forth. There are no other forces in the system. At what point is the block moving the fastest?
More Gravitational Force Questions:
g on different planets
Practice: Acceleration Due to Gravity on Different Planets
Earth has radius RE (6371 km) and mass ME (5.97*1024 kg). The gravitational acceleration at the surface is given by g=GMR2g=G\frac{M}{R^2}(G = 6.67*10-11 Nm2/kg2).
What would the gravitational acceleration on the following planets be? Give your answer in terms of g.
Practice: Newton’s Law of Universal Gravitation
Practice: Newton's Law of Universal Gravitation
The Earth has mass 5.927 x 1024 kg and radius 6371 km. How far above the Surface of the Earth would a 50 kg person have to go in order for his weight to be 15 % less than it is at the surface?
Kepler's third law example
Practice: Satellite (Orbital Period)
Some bright students are planning to send a satellite to orbit around the earth at an altitude of 4000.0 km above the surface. What will be the orbital period of this satellite? (answer in seconds)
Practice: Satellite Orbiting Earth
A 600 kg satellite and a 450 kg satellite are in orbit around the Earth. The 600kg satellite is at a distance of 2000 km from the Earth’s surface while the 450 kg satellite is at a distance of 15 000 km.
a) What is period of the satellites?
Kepler's third law example
Some bright students are planning to send a satellite to orbit around the earth at altitude of 4000 km above the surface. What will be the orbital period of this satellite?
Because of Earth's rotation about its axis, a point at the poles has no centripetal acceleration. (Assume Earth is a uniform sphere and take g=9.800 ms2. g=9.800\ \frac{m}{s^2}.\ )
A 5000kg satellite is in orbit around the Earth and has an orbital radius of 35 900 km.
a) What is the magnitude of the force that the satellite exerts on the Earth? (mass of Earth = 5.98 x 1024 kg)
b) By what proportion does the force change if the satellite's mass is cut by 75% and the orbit height cuts in half?
Three identical point masses, each of 3.41 kg are located at the corners of an equilateral triangle of side length 1.5 m.
a) Consider a point halfway along one of the sides. What would be the direction of the net force at this point if we put another mass there? (Hint: Always start physics problems by drawing a picture!)
b) What is the net force on one of the three masses? (Remember: force is a vector, so your answer should have a magnitude and a direction.)
Practice: Measuring gravity
You set up a simple experiment to measure gravitational acceleration on Earth. You drop a ball from 14 feet above the ground (a second-floor window). You use a stopwatch to find that it falls from rest in 1.013 seconds. Calculate Earth's gravitational acceleration based on these results to the appropriate number of significant figures, and comment on your result with one suggestion for improving the experiment. (one foot=0.305 meters)
Practice: Mars Rock Drop
A martian drops a rock from a height of 8.71 meters on Mars, where gravitational acceleration near the planet's surface is 3.711 m/s2.
g on different planets
Earth has radius RE (6371 km) and mass ME (5.97*1024 kg). The gravitational acceleration at the surface is given by g=GMR2g=G\frac{M}{R^2}(G = 6.67*10-11 Nm2/kg2).
What would the gravitational acceleration on the following planets be? Give your answer in terms of g.
a) Mercury (M = 0.055ME, R = 2440 km)
A 600 kg satellite and a 450 kg satellite are in orbit around the Earth. The 600kg satellite is at a distance of 2000 km from the Earth’s surface while the 450 kg satellite is at a distance of 15 000 km.
a) What is period of the satellites?
b) What is their speed?
Kepler's third law example
Some bright students are planning to send a satellite to orbit around the earth at altitude of 4000.0 km above the surface. What will be the orbital period of this satellite? (answer in seconds)
Practice: Newton’s Law of Universal Gravitation
The Earth has mass 5.927 x 1024 kg and radius 6371 km. How far above the Surface of the Earth would a 50 kg person have to go in order for his weight to be 15 % less than it is at the surface?
Getting Earth out of orbit
The Sun is about to explode. We need to get the Earth out of the solar system.
Radius and mass of the Sun is 6.95 x 108m and 1.99 x 1030kg. Radius and mass of the Earth is 6.37 x 106m and 5.97 x 1024kg.
Escape from Mars
You are in a spaceship that's moving at 4.20 x 103m/s at an altitude of 254km above the surface of Mars. The mass of Mars is 6.46 x 1023kg and radius is 3.39 x 106m. Will you be able to get into space or will you fall back to the planet?
Satellite into space
How much energy do we need to send a 9000.0 kg satellite from the Earth to the ISS, which is at 4.00 x 105m above the Earth's surface? You are given the mass of the Earth (5.98 x 1024kg), the radius of the Earth (6.37 x 106m). Answer in Joules.
Moon's orbit
Given the mass of the Earth (5.98 x 1024kg), the radius of the Earth (6.37 x 106m), the mass of the moon (7.35 x 1022kg) and the radius of the moon (1.74 x 106m).
a) Calculate the magnitude of the acceleration of the moon due to the Earth's gravity. The distance to the moon is 3.84 x 108 m.
b) Calculate the centripetal acceleration if the moon is in a circualr orbit. The period of the moon's orbit is 2.73 days.
The acceleration due to gravity depends on the...
A particle with mass m1 = 20 kg, is at the origin, the second particle with mass m2= 30 kg is at −2ȷ^-2\hat\jmath and the 3rd mass with m3= 5 kg is at 3ı^+4ȷ^3\hat\imath+4\hat\jmath .
What is the gravitational force between m2 and m3? What is the total gravitational force on m3?
Practice: Percent Error
An experiment finds that the acceleration due to gravity is 10.2m/s2. What is the percentage error in this experiment? Use g=9.8m/s2 as the accepted value for gravity.
Three identical point masses, each of 3.41 kg are located at the corners of an equilateral triangle of side length 1.5 m. What is the net force on one of the masses?
A satellite circles the earth at an altitude of approximately 20,000 km, where the gravitational acceleration is 5.8% of its surface value. Find the orbital period of the satellite.
Three identical point masses, each of 3.41 kg are located at the corners of an equilateral triangle of side length 1.5 m. What is the net force on one of the masses?