Dynamics: Physics 9702 (Cambridge International AS & A Level)

A book of weight $12\text{ N}$ rests in equilibrium on a horizontal table. The table exerts a normal contact force of $12\text{ N}$ vertically upward on the book.

Which force forms the Newton's third law reaction pair to this $12\text{ N}$ contact force that the table exerts on the book?

A warehouse robot of mass $12\text{ kg}$ moves across a flat, horizontal concrete floor. A motor inside the robot provides a constant horizontal driving force of $30\text{ N}$ in its direction of travel, while a constant resistive force of $6.0\text{ N}$ (from friction and air resistance) acts on the robot in the opposite direction.

Take $g = 9.81\text{ m s}^{-2}$.

(a) Calculate the weight of the robot. [1]

(b) Determine the magnitude of the resultant horizontal force acting on the robot while the driving force is switched on. [2]

(c) Use Newton's second law to calculate the robot's acceleration while the driving force is switched on. [2]

(d) The driving force is then switched off, while the $6.0\text{ N}$ resistive force continues to act. Calculate the magnitude of the robot's new acceleration, and state its direction relative to the robot's direction of travel. [1]

Trolley $A$, of mass $0.40\text{ kg}$, travels at $1.8\text{ m s}^{-1}$ along a horizontal, frictionless air track and collides with trolley $B$, of mass $0.60\text{ kg}$, which is initially at rest on the same track. The two trolleys have magnetic pads that lock together on impact, so immediately after the collision they move off with a single common velocity.

(a) Calculate the common velocity of the two trolleys immediately after the collision. [2]

(b) By calculating the total kinetic energy of the system immediately before and immediately after the collision, determine whether the collision is elastic or inelastic. [3]

(c) Explain why the linear momentum of the two-trolley system is conserved in this collision, even though kinetic energy is not conserved. [2]

Two ice hockey pucks collide on a frictionless, horizontal ice rink. Puck $A$ has mass $0.30\text{ kg}$ and travels at $5.0\text{ m s}^{-1}$ due east. It strikes puck $B$, of mass $0.50\text{ kg}$, which is initially at rest.

Immediately after the collision, puck $A$ moves off at $3.0\text{ m s}^{-1}$, at an angle of $53.1°$ measured from due east, on the north side of the original line of travel.

Take east as the positive $x$-direction and north as the positive $y$-direction.

(a) Calculate the $x$- and $y$-components of the total momentum of the two-puck system before the collision. [2]

(b) Use conservation of momentum in the $x$- and $y$-directions to find the velocity of puck $B$ immediately after the collision. Give your answer as a magnitude and a direction relative to due east. [4]

(c) By calculating the total kinetic energy of the system immediately before and immediately after the collision, determine whether the collision is elastic or inelastic. [2]

A small ball of mass $0.50\text{ kg}$ is initially at rest on a smooth horizontal surface. A constant resultant force of $4.0\text{ N}$ acts on the ball for a time of $3.0\text{ s}$, after which the force is removed.

What is the magnitude of the ball's momentum at the instant the force is removed?

Trolley $P$, of mass $2.0\text{ kg}$, is connected by a light, inextensible string to trolley $Q$, of mass $3.0\text{ kg}$, which follows behind it. Both trolleys are on a horizontal track which may be assumed frictionless. A constant horizontal force of $15\text{ N}$ is applied to trolley $P$, pulling both trolleys forward together.

(a) Calculate the acceleration of the two trolleys. [2]

(b) Calculate the tension in the string connecting the two trolleys. [3]

(c) The string suddenly breaks while the trolleys are moving. State the magnitude of the resultant horizontal force now acting on trolley $Q$, and describe its subsequent motion. [2]

A ball of mass $0.20\text{ kg}$ travels horizontally at $8.0\text{ m s}^{-1}$ and strikes a wall at right angles. It rebounds directly back along its original path at $6.0\text{ m s}^{-1}$. The ball is in contact with the wall for $0.050\text{ s}$.

What is the magnitude of the average force exerted by the wall on the ball?

Trolley $C$, of mass $0.20\text{ kg}$, travels at $6.0\text{ m s}^{-1}$ along a frictionless horizontal air track and collides with trolley $D$, of mass $0.40\text{ kg}$, which is initially at rest on the same track. The collision between the trolleys is perfectly elastic.

(a) State the two conditions that must both be satisfied for a collision to be described as perfectly elastic. [2]

(b) For a perfectly elastic collision, the relative speed of approach of the two bodies equals their relative speed of separation. Use this fact, together with conservation of momentum, to determine the velocity of each trolley immediately after the collision. Take the direction of trolley $C$'s initial motion as positive. [4]

(c) By calculating the total kinetic energy of the system immediately before and immediately after the collision, verify that the collision is indeed perfectly elastic. [2]

A space probe of total mass $900\text{ kg}$ is at rest in deep space, far from any other body, so no external resultant force acts on it. An internal explosive charge separates the probe into two parts: a lander of mass $200\text{ kg}$ and a service module of mass $700\text{ kg}$. Immediately after separation, the lander moves away at $12\text{ m s}^{-1}$.

(a) State the total momentum of the probe immediately before separation, and explain why the total momentum of the two parts must be the same immediately after separation. [2]

(b) Calculate the velocity of the service module immediately after separation, stating its direction relative to the motion of the lander. [3]

(c) Calculate the total kinetic energy of the two parts immediately after separation, and state the origin of this energy. [3]

A car of mass $800\text{ kg}$ starts from rest and accelerates in a straight line to a speed of $20\text{ m s}^{-1}$ in a time of $8.0\text{ s}$.

What is the magnitude of the average resultant force acting on the car during this time?