Circular Motion and Gravitation

The acceleration of gravity experienced by objects located near to (and far from) from the earth depends upon the mass of the object.

A is false; check out the equation - g = GMcentral/R2. The value of g does not depend upon the object's mass.

The acceleration of gravity experienced by objects located near to (and far from) from the earth depends upon the mass of the Earth.

B is true; check out the equation again. The acceleration of gravity created by the earth depends upon the earth's mass.

The acceleration of gravity experienced by objects located near to (and far from) the earth is inversely related to the distance between the center of the object and the center of the earth.

C is true; check out the equation one more time. The separation distance is located in the denominator of the equation, indicating an inverse relationship.

Increasing the mass of an object will increase the acceleration of gravity experienced by the object.

D is false; like statement A, this statement makes a claim that the acceleration of gravity depends upon the mass of the object. It does not. In the derivation of g from the Universal Gravitation equation, the mass cancels. :)

Doubling the distance between an object and the earth's center will decrease the acceleration of gravity by a factor of four.

E is true; g is inversely proportional to the square of the distance; a doubling of the distance means that you must divide the force of gravity value by 4 (22) to obtain the new force of gravity value.

The acceleration of an orbiting satellite is equal to the acceleration of gravity at that particular location.

F is true; the acceleration of gravity is the acceleration which is caused by gravity when it is the only force. For an orbiting satellite, gravity is the only force.

If the mass of the Earth were doubled (without an alteration in its radius), then the acceleration of gravity on its surface would be approximately 20 m/s2.

G is true; according to the equation, the g value is directly proportional to the mass of the earth. An increase in M results in a proportional increase in g.

If the mass of the Earth were doubled and the radius of the earth were doubled, then the two changes would offset each other and the acceleration of gravity on its surface would still be approximately 10 m/s2.

H is false; g is approximately 10 m/s/s on earth's surface. Doubling the mass of the earth would increase g to approximately 20 m/s/s. Then doubling the distance from the surface of the earth to its center would decrease g by a factor of 4. The new acceleration of gravity value would be approximately 5 m/s/s. Clearly, these two alterations do not offset each other.

12. How did Newton come up with the idea that the moon is actually "falling" toward the Earth.

Newton made the connection between objects falling (accelerating) towards the earth and objects in space which are accelerating towards the earth while they are in circular motion around the earth. Both are being pulled by the earth due to the gravitational force. The moon stays in orbit due to it having the appropriate tangential velocity that keeps it from coming closer to the earth's surface. The moon, however, is still accelerating at the rate any object would have at that distance from the earth. In a sense, the moon is falling around the earth rather than into the earth.

9. Which of the following statements are true about satellites? Identify all that apply.

Satellites are falling projectiles. Satellites travel faster along their orbital path when they are closest to the earth. The acceleration of a satellite varies inversely with its distance from the center of the earth. More distant satellites have smaller accelerations.

10. Which of the following statements are true about the motion of planets about the sun? Identify all that apply.

The force of gravity is the only force which acts upon the planets. The planets which are furthest from the sun have the greatest period. For any given planet, the speed is greatest when the planet is closest to the sun. The velocity vector is directed tangent to the elliptical path.

11. Explain how something can be moving at a constant speed yet be accelerating at the same time.

The object would have to be traveling in a curved path since it is accelerating. Acceleration is defined as a change in velocity over a change in time. If the speed is staying the same, then the velocity must be changing by altering the direction in which the object is heading. A force is required to do this.

Which of the following statements are true of an object moving in a circle at a constant speed?

There can be a force pushing outwards on the object as long as the net force in inwards. If the net force acting upon the object is suddenly reduced to zero, then the object would suddenly depart from its circular path and travel tangent to the circle.

14. Describe the apparent weight of a person in an elevator while upward, accelerating downward, and not accelerating.

When one stands upright on a scale, the scale measures the force of the scale pushing upwards on the body. As such, the scale does not measure one's true weight, but one's apparent weight. An elevator accelerating someone up must not only apply a force to provide the acceleration but also oppose the gravitational force on the person. Therefore, a scale would register a number larger than the gravitational force if the person is accelerating upward. In this case, a person would experience an apparent weight which is greater than usual. Likewise, if the person is accelerating downward the scale reading must be less than the gravitational force since the gravitational force is accelerating them downward. As such, the person's apparent weight is less than what they are accustomed to experiencing. If the elevator is moving at constant velocity or at rest, the scale reading must match the gravitational force in order to have a net force of 0. The apparent weight would be equal to the actual weight of the person.

The doubling of the separation distance (measured from the center) between two objects will halve the gravitational force between the objects.

false; doubling the separation distance will make the force one-fourth the size.

The gravitational force between two objects is independent of the mass of the smaller of the two objects.

false; gravitational force is dependent upon the product of the two masses. Both masses are important in the computation.

The gravitational force only acts between very, very massive objects.

false; gravitational forces are universal (Newton's big idea); they act between any two objects which have mass.

Orbiting astronauts do not experience a force of gravity; this explains why they feel weightless.

false; orbiting astronauts must be experiencing the force of gravity. Without this force, there would be no centripetal force and no orbit.

If an object is placed two earth-radii above the surface of the earth, then the force of gravitational attraction between the object and the earth will be one-fourth the magnitude as on earth's surface.

false; placing the object at two earth-radii above earth's surface will put 3-earth radii from earth's center. This is equivalent to increasing the separation distance by a factor of 3; this decreases the force by a factor of 9.

A car makes a sharp right-hand turn along a level roadway.

friction

The moon orbits the earth.

gravity

A roller coaster car passes through a loop. Consider the car at the bottom of the loop.

normal

An eraser is tied to a string swung in a horizontal circle.

tension

If object A gravitationally attracts object B with a force of X Newtons, then object B will also gravitationally attract object A with the same force of X Newtons.

true; for every action there is an equal and opposite reaction. This is Newton's third law, an inescapable reality about forces.

The gravitational force between an object and the earth is inversely related to the distance between the object's and the earth's center.

true; if the distance is increased, then the force is decreased.

The gravitational force can ALWAYS be accurately calculated by multiplying the object mass by the acceleration of gravity (m•g).

true; this is always the case. It is not true however to say that the gravitational force is equal to mass•9.8 m/s/s. The value of g varies with location and so at distances significantly further from the earth's surface, g is reduced and the gravitational force must be computed using a different value of g.

The gravitational force acting upon an object is the same as the weight of the object.

true; weight and gravitational force are synonymous.