Forces and momentum practice questions.

For a satellite in a circular orbit around a planet, the gravitational attraction of the planet provides the

• centripetal force
• tangential driving force
• frictional force
• upward lift force

Answer: centripetal force

Gravity acts towards the centre of the orbit, providing exactly the centripetal force needed to keep the satellite moving in a circle at constant speed.

A ball on the end of a string is swung in a horizontal circle at constant speed. The speed of the ball is doubled while the radius of the circle is kept the same. By what factor does the tension in the string change?

• It becomes four times as large.
• It becomes twice as large.
• It becomes half as large.
• It is unchanged, because the radius has not changed.

Answer: It becomes four times as large.

The tension provides the centripetal force F = mv²/r, which depends on the square of the speed, so doubling v multiplies the force by 2² = 4. Answering “twice” treats a squared relationship as a linear one — the single most common proportionality error in circular motion.

A book lies at rest on a horizontal table. Which force is the Newton's third law pair of the weight of the book?

• The normal force of the table on the book, acting on the book.
• The downward push of the book on the table, acting on the table.
• The weight of the table itself, which acts on the table and not on the book.
• The gravitational pull of the book on the Earth, acting on the Earth.

Answer: The gravitational pull of the book on the Earth, acting on the Earth.

A third law pair is the same kind of force, between the same two bodies, acting on the other one. The weight is gravitational and is exerted by the Earth, so its partner is the book's gravitational pull on the Earth. The normal force is a contact force and equals the weight only because this particular book happens to be in equilibrium.

A raindrop falls from rest through still air and eventually reaches a terminal speed. Which statement describes the raindrop at the instant when its speed is half the terminal speed?

• The drag force equals the weight, so the raindrop already falls at constant speed.
• The drag force is smaller than the weight, so the raindrop is still speeding up.
• The drag force exceeds the weight, so the raindrop is slowing down as it falls.
• The drag force is still zero, so the raindrop accelerates at the free-fall value.

Answer: The drag force is smaller than the weight, so the raindrop is still speeding up.

Drag grows with speed, so below the terminal speed it has not yet grown large enough to balance the weight: the resultant force is downward and the acceleration is smaller than g but not zero. Terminal speed is defined by drag = weight, which is precisely the condition that has not been reached.

The resultant force on a tennis ball during a serve varies with time and is plotted as a smooth curve. Which quantity is given by the area between that curve and the time axis?

• The work done on the ball, and hence its change in kinetic energy.
• The average resultant force acting on the ball during the contact.
• The rate of change of momentum of the ball during the contact.
• The impulse on the ball, and hence its change in momentum.

Answer: The impulse on the ball, and hence its change in momentum.

Force multiplied by time is impulse whatever the shape of the curve, and impulse equals the change in momentum. Force multiplied by displacement — not by time — would give the work done, and the rate of change of momentum is the height of this graph, not its area.

Two perpendicular forces of 3.0 N and 4.0 N act on a point. What is the magnitude of their resultant (in N)?

Answer: 5

For perpendicular vectors use Pythagoras: R = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.0 N.