6 Circular Motion

Question 1

gravitational field

Answer 1

A region of space where a test mass experiences a force due to the gravitational attraction of another mass

Question 2

gravitational field strength

Answer 2

force per unit mass;
on a point mass

Question 3

gravitational potential energy [J]

Answer 3

work done to move a body;
from infinity to a point in the gravitational field

Question 4

electric potential energy [J]

Answer 4

work done to move the charges;
from infinite separation to their current positions in the electric field

Question 5

gravitational potential
V [J kg-1]

Answer 5

work done per unit mass;
in bringing a point mass;
from infinity to a point in the gravitational field

Question 6

electric potential, V [J C-1]

Answer 6

work done per unit charge;
in bringing a test charge;
from infinity to a point in the electric field

Question 7

escape speed

Answer 7

speed of object at a planet’s surface; to escape from the gravitational field and travel to infinity

Question 8

Newton’s Universal Law of Gravitation

Answer 8

F = GMm/r²
the force of gravity between two objects is inversely proportional the square of the separation of their centres and directly proportional to the product of their masses

Question 9

describe circular motion in terms of a puck stretched by a string

Answer 9

The stretched string applies a centripedal force –> centripedal force is perpendicular to velocity, so there is no component of force in the direction of the velocity –> no acceleration in the direction of the velocity –> puck moves in a circle around the center with constant speed

Question 10

period, T, of circular motion

Answer 10

time taken for the object to complete 1 rotation (2π radians)

Question 11

angular displacement

Answer 11

∆θ = S/r
the change in angles of a body (in radians) as it rotates in a circle

Question 12

angular speed

Answer 12

ω = ∆θ/∆t
the rate of change in angular displacement with respect to time

Question 13

centripetal Force

Answer 13

The resultant force directed towards the centre of the circle (perpendicular to velocity) , which keeps a body in uniform circular motion

Question 14

centripetal acceleration

Answer 14

The resultant acceleration directed towards the centre of the circle (perpendicular to velocity) when an object is moving in a circle at a constant speed

Question 15

calculated the maximum speed at which a car can travel around a curved road without skidding

Answer 15

centripetal force = friction
mv²/r = µmg
→ v = √µgr

Question 16

as you swing a ball on a string in a vertical circle,
- what is the max tension needed?
- what is the min tension needed?
- at which point is the speed of the ball fastest?

Answer 16

Tmax = mv²/r + mg (occurs at the bottom where T need to overcome mg AND provide centripetal force)

Tmin = mv²/r - mg (occurs at the top where mg already provides partial centripetal force and T only need to provide the rest)

since the acceleration is max at the bottom, the speed is also max at the bottom

Question 17

Does the mass of a satellite affect the velocity it orbits the Earth?

Answer 17

No.
GMm/r² = mv²/r
the m cancels out, leaving v² = GM/r

Question 18

Derive Kepler’s 3rd Law

Answer 18

v² = (2πr/T)² = GM/r
4π²r² /T² = GM/r
4π² r³ = GMT²
r³∝ T²

Question 19

The Earth’s gravitational field always produces an … force

Answer 19

attractive

Question 20

what are the factors that influence gravitational field strength g? derive using equation

Answer 20

mg = GMm/r²
cancel the m, we get
g = GM/r²
therefore, gravitational field strength g only depends upon M, the mass that causes the field, and r, the distance from the mass where we are calculating the field strength

Question 21

frequency, f, of circular motion

Answer 21

the number of rotations in unit time (f = 1/T)

Question 22

A girl is playing on a swing.
1. What is providing the centripetal force on the swing seat?
2. What is providing the centripetal force on the girl?
3. Draw a free-body diagram to show the forces acting on the girl

Answer 22

1. tension in the swing chain
2. normal reaction force from swing seat
3. mg下, N斜左上，friction斜右上！！

Question 23

What is providing the centripetal force on the swing seat?

Answer 23

a component of the normal force from the air (lift) pushing the plane’s tilted wings

Question 24

What provides the centripetal force for these athletes running on a curved track?

What design features make sure that this force can be large enough for high speeds?

Answer 24

friction between the track and their shoes

the track needs high friction coefficient + can deform elastically

Question 25

How can a beam of alpha particle be made to move in a circular path?

Answer 25

direct it perpendicularly across a uniform magnetic field

Question 26

Does the gravitational forces between the Earth and the Moon have any noticable effect on the Earth?

Answer 26

tides on the oceans

Question 27

Explain why it is very difficult to measure gravitational forces

Answer 27

gravitational forces on everyday objects are very small → technical difficulty to measure as other forces may also be acting (eg. electric, magnetic)

Question 28

which equation do you use for this question:
Two planets orbit the same star at distances of 4.8 × 10^10 m and 7.9 ×10^11 m. If the first planet has a period of 200 Earth days, what is the period of the second?

Answer 28

Kepler’s 3rd Law:
r³/T² = constant

Question 29

which equation do you use for this question: What is the required orbital speed for a satellite designed to circle the Earth at a height of 1000km?

Answer 29

v² = GM/r

Question 30

mass of Earth

Answer 30

5.97 x 10^24

Question 31

Calculate the distance from the centre of the Earth to a satellite which has a period of 24h.

Answer 31

只要跟r和T有关的都用Kepler’s 3rd Law！
r³/T² = GM/4π²