Chapter 6 Quiz Circular Motion and Gravitation
Fullname:……………………………………………………………………………………………………………………………………Date: 11/4/22
1. A small ball of mass m is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.
The normal reaction force N makes an angle θ to the horizontal.
a) State the direction of the resultant force on the ball.
b) On the diagram, construct an arrow of the correct length to represent
the weight of the ball.
c) Show that the magnitude of the net force F on the ball is given by the
following equation.
d) The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the
ball
2. An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω.
What is the tension in the string when the object is at the bottom of the circle?
3. A satellite powered by solar cells directed towards the Sun is in a polar orbit about the Earth.
The satellite is orbiting the Earth at a distance of 6600 km from the centre of the
Earth.
Determine the orbital period for the satellite.
Mass of Earth = 6.0 x 1024 kg
4. A small ball of weight W is attached to a string and moves in a vertical circle of radius R
The minimum speed at the smallest highest point of the ball is 𝑣.
What is the kinetic energy at the lowest point? Express the result in
terms of the weight and radius of the circumference.
5. Two satellites of mass m and 2m orbit a planet at the same orbit radius. If F is the force exerted on the satellite
of mass m by the planet and a is the centripetal acceleration of this satellite, what is the force and acceleration
of the satellite with mass 2m?
6. Point X is a distance 2L from the centre of the disc. Point Y is a distance L from the centre of the disc.
Point Y has a linear speed v and a centripetal acceleration a.
What is the linear speed and centripetal acceleration of point X?
7. A mass is suspended by a string from a fixed point. The mass moves with constant speed along a circular path in
a horizontal plane.
Find the acceleration as a function of the angle
8. This question is about gravitation and uniform circular motion.
Phobos, a moon of Mars, has an orbital period of 7.7 hours and an orbital radius of 9.4 × 103 𝑘𝑚
a)
b)
c)
9.
Outline why Phobos moves with uniform circular motion.
Show that the orbital speed of Phobos is about 2 kms−1
Deduce the mass of Mars
An object rotates in a horizontal circle when acted on by a centripetal force F. What is the centripetal force
acting on the object when the radius of the circle doubles and the kinetic energy of the object halves?
10. The centre of the Earth is separated from the centre of the Moon by a distance D. Point P lies on a line
joining the centre of the Earth and the centre of the Moon, a distance X from the centre of the Earth. The
gravitational field strength at P is zero.
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑀𝑜𝑜𝑛
What is the ratio 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝐸𝑎𝑟𝑡ℎ
11. The centres of two planets are separated by a distance R. The gravitational force between the two planets is F.
What will be the force between the planets when their separation increases to 3R?
12. The mass of Earth is ME, its radius is RE and the magnitude of the gravitational field strength at the surface of
Earth is g. The universal gravitational constant is G. The ratio g/G is equal to
13. A planet has radius R. At a distance h above the surface of the planet the gravitational field strength is g
and the gravitational potential is V.
State what is meant by gravitational field strength.
Show that V = –g(R + h).
Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height
h above the surface of the planet