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Supplemental Questions
A billiard ball of mass 0.17 kg rolls toward the right-hand cushion of a billiard table at 2.1 m/s, then
rebounds straight back at 1.8 m/s.
(a) What is the change in momentum of the ball as a result of hitting the cushion?
(b) What impulse does the cushion give to the ball?
Two ice skaters, initially stationary, push each other so that they move in opposite directions. One skater of
mass of 56.9 kg has a speed of 3.28 m/s. What is the mass of the other skater if her speed 3.69 m/s? Neglect
friction.
A rocket has a constant force of 3.85x105 N and an initial speed of 1.22x104 kg. If the rocket applies that
force over a distance of 2.45x106 m, determine the final speed.
A 1.37-kg fish is hung from a vertical spring scale with a force constant of 5.20x10² N/m. The spring obeys
Hooke’s Law.
(a) By how much does the spring stretch if it stretches slowly to a new equilibrium position?
(b) If the fish is attached to the un-stretched spring scale and allowed to fall, what is the net force on the
fish when it has fallen 1.59 cm?
(c) Determine the acceleration of the fish after it has fallen 2.05 cm.
A child’s toy shoots a rubber dart of mass 7.8 g, using a compressed spring with a force constant of 3.5x10²
N/m. The spring is initially compressed 4.5 cm. All the elastic potential energy is converted into the kinetic
energy of the dart.
(a) What is the elastic potential energy of the spring?
(b) What is the speed of the dart as it leaves the toy?
In a game, a small block is fired from a compressed spring up a plastic ramp into various holes for scoring.
The mass of the block is 3.5x10ˉ³ kg. The spring’s force constant is 9.5 N/m. Friction is negligible.
(a) If the block is to slide up the ramp through a vertical height of 5.7 cm, by how much must the spring
be compressed?
(b) If friction were negligible, would your answer in (a) increase, decrease, or remain the same. Explain?
The maximum energy of a mass-spring system undergoing SHM is 5.64 J. The mass is 0.128 kg and the
force constant is 244 N/m.
(a) What is the amplitude of the vibration?
(b) Use two different approaches to determine the maximum speed of the mass.
(c) Find the speed of the mass when it is 15.5 cm from the equilibrium position.
A nitrogen molecule of mass 4.65x10ˉ²⁶ kg in the air undergoes a head-on elastic collision with a stationary
oxygen molecule of mass 5.31x10ˉ²⁶ kg. After the collision, the nitrogen molecule has reversed its direction
and has a speed of 34.1 m/s, while the oxygen molecule is travelling 4.81x10² m/s in the original direction of
the nitrogen molecule. What is the initial speed of the nitrogen molecule?
A proton travelling with an initial speed of 815 m/s collides head-on with a stationary proton in an elastic
collision. What is the velocity of each proton after the collision? Show your work.
(a) What is the speed of the swinging ball just before the collision?
(b) What is the speed of the 0.21 kg ball just after the collision?
A 0.25-kg ball is attached to a 26 cm piece of string. The ball is first raised so that the string is taut and
horizontal, then the ball is released so that, at the bottom of its swing, it undergoes an elastic head-on
collision with a 0.21 kg ball that is free to roll along a horizontal table.
(c) What is the speed of the swinging ball just before the collision?
(d) What is the speed of the 0.21 kg ball just after the collision?