Circular Motion & Gravitation — practice questions

A $0.20$ kg ball on a string moves in a horizontal circle of radius $0.50$ m at $3.0$ m s⁻¹.

Show that the centripetal force is $3.6$ N.

A car of mass $900$ kg rounds a flat (unbanked) corner of radius $40$ m at $15$ m s⁻¹.

Calculate the friction force needed, and state what provides the centripetal force.

A bucket of water of mass $1.2$ kg is swung in a vertical circle of radius $0.90$ m.

Determine the minimum speed at the top for the water to stay in the bucket, and explain what happens to the normal (contact) force at that speed.

Two $1.0 \times 10^{3}$ kg masses are $2.0$ m apart (centre to centre).

Show that the gravitational force between them is about $1.7 \times 10^{-5}$ N. ($G = 6.67 \times 10^{-11}$ N m² kg⁻².)

A satellite orbits a planet of mass $6.4 \times 10^{23}$ kg at a radius of $3.8 \times 10^{6}$ m.

Calculate its orbital speed. ($G = 6.67 \times 10^{-11}$ N m² kg⁻².)

Explain why a geostationary satellite must orbit at one particular radius, and why it can only sit above the equator.