High School
SAT
ACT
University
MCAT
LSAT
DAT

Because of Earth's rotation about its axis, a point at the poles has no centrip…

Related Topics

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

Gravitational Force

4 Activities

Wize University Physics Textbook (Master) > Circular Motion

Centripetal Acceleration and Centripetal Force

4 Activities

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}.\ )
checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
(a) Show that, at the equator, the gravitational force on an object (the object's true weight) must exceed the object's apparent weight.
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?
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.)
Simple Harmonic Motion: Pendulum
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)
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?
More Centripetal Acceleration and Centripetal Force Questions:
Two strings on a spinning rod - solving
Practice: Two Strings on Spinning Rod
The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 80.0 N.
Vertical circular motion
Practice: Vertical String
A box of mass 2.50 kg is attached to a string and whirled in a vertical circle of radius 1.0 m. At the exact top of the path, the tension in the string is 3 times the ball’s weight.
Ball on a string at an angle
Practice: Ball on String at an Angle
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
A wheel of radius 14.0 m is turning about a horizontal axis through its center. The linear speed of a passenger on the rim is constant and equal to 7.00 m/s.
(a) What are the magnitude and direction of the passenger's acceleration as she passes through the lowest point in her circular motion?
(b) Repeat part (a), but for the highest point instead of the lowest.
Ball on a string at an angle
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
A puck of mass m slides on a frictionless table while attached to a hanging cylinder of mass M by a cord through a hole in a table. What is the angular momentum of the puck?
(Hint: find the speed of the puck by considering uniform circular motion - what is the force providing the centripetal acceleration?)
Practice: Sliding off of a globe
A child is sliding on a spherical pile of snow of radius R. The child is initially at rest at the very top of the hemisphere, but is given a slight push to start sliding down. Neglect friction.
Energy conservation and circular motion
A compressed spring is used to propel a 25-gram ball-bearing along a frictionless horizontal track which contains a circular vertical loop of radius 0.30 m in a vertical plane. The spring obeys Hooke's law and is compressed 20 cm by a force of 5.0 N.
a) What is the speed of the ball-bearing at the top of the loop? Treat the ball bearing as a point mass.
b) What is the minimum spring compression required to have the ball-bearing complete a full loop?
Tension and centripetal force
The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 80.0 N.
Two strings on a spinning rod - setup, approach
The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 80.0 N.
Set up the problem (a free-body diagram, find unknown angles and distances, define coordinates) and then go to the next activity. Ask yourself: how do we deal with the rpm quantity in part (b)?
Vertical circular motion
A box of mass 2.50 kg is attached to a string and whirled in a vertical circle of radius 1.0 m. At the exact top of the path, the tension in the string is 3 times the ball’s weight.
For the following systems, draw free-body diagrams and explain what real force(s) is/are providing the centripetal force.
The moon orbiting around the earth
Being in the Gravitron amusement ride (inside, the people are stuck against the walls while the ride spins extremely fast - see picture below)
A small car with mass 0.800 kg travels at constant speed on the inside of a track that is a vertical circle with radius 5.00 m (Fig.). If the normal force exerted by the track on the car when it is at the top of the track (point B) is 6.00 N, what is the normal force on the car when it is at the bottom of the track (point A)
Driving in a circle
You are driving around a sharp corner, going clockwise. There is a box in the middle of your back seat. If you are driving fast enough, the box will slide to a side of your car. Which side will it slide to? Why?
(Hint: even if questions do not ask you to draw a sketch or picture, you should draw one anyway! It makes life easier for both you and the exam marker.)
air puck problem
An air puck of mass m1=0.25 kg{\small m_1=0.25\ kg} is tied to a string and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of string passes through a hole in the center of the table, and a mass of m2=1.0 kg{\small m_2=1.0\ kg} is tied to it (Fig.). The suspended mass remains in equilibrium while the puck on the tabletop revolves.
Ball on a string at an angle
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
Circular Motion
A 20-g marble is free to slide on a frictionless wire loop with radius of 15 cm. The loop starts to rotate about its vertical axis until the bead slides up to θ=60∘ as shown below. What is the angular velocity of the loop at this moment?
A point object travelling in a circle must always have a net force acting on it.
Centripetal force
When an object experiences uniform circular motion, the direction of the net force is
A ball of mass 5 kg and charge Q is performing uniform circular motion on a horizontal surface. The radius of rotation is R=1m and the period of rotation is T=5 s.
If the ball is attached to a spring with equilibrium length of 0.5 m, what is the spring constant?
Assume we put another charge with the same magnitude at the origin for maintaining the circular motion. What is the type and magnitude of the charge?
The 4.00-kg block is Fig. is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown is the diagram and the tension in the upper string is 80.0 N. (a) What is the tension in the lower cord ? (b) How many revolutions per minute does the system make ? (c) Find the number of revolution per minute at which the lower cord just goes slack. (d) Explain what happens if the number of revolutions per min is less than in part c.
In the 'Giant swing' , the seat is connected to two cables as shown in Fig. , one of which is horizontal.The seat swings in a horizontal circle at a rate of 32.0 rpm (rev/min).If the seat weighs 255 N and an 825 N person is sitting in it, find the tension in each cable.
A boy standing in one spot swings a box on a string in a horizontal circle of radius 2m around him as fast as he can. If the force of tension in the string is 100 N and the mass of the box is 30kg, how fast is the box moving? How many revolutions per minute does it make?
A ball of mass M is released from rest at a vertical height h above the ground. The ball rolls down a frictionless inclined plane and makes it to a loop the loop of radius R.
What is the velocity of the ball as it reaches to the bottom of the incline?
What is the normal force at the bottom?
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
If the angle that the string makes with the vertical increases, what happens to the ball speed?
Vehicles must be able to traverse a curve of radius 60.0 m safely at speeds up to 80 km/h. If the average vehicle weighs 1000 kg, what minimum coefficient of friction is required to make this possible?
A 65 kg man is riding a Ferris wheel with radius of 15 m, that moves at 1.5 rpm. Determine the normal force that the man experiences at the top of the ferris wheel and at the bottom.
A boy standing in one spot, swings a box on a string in a horizontal circle with the radius of 2m around him as fast as he can. If the force of tension in the string is 100 N and and the mass of the box is 30kg, how fast is the box moving? How many revolutions per minute does it make?