Forces & Momentum (DP IB Physics)

True.

According to Newton's first law of motion, an object at rest will remain at rest unless acted upon by a resultant force.

An object is in translational equilibrium if the vector sum of all the forces acting on it are zero, and therefore there is no resultant force.

According to Newton's first law, a body travelling at a constant velocity would remain travelling at that constant velocity if no resultant force acted upon it. There would be no change in the object's motion.

The three ways that a resultant force can change an object's motion are:

• speed it up (accelerate)

• slow it down (decelerate)

• change its direction

Newton's second law of motion states that the resultant force on an object is directly proportional to its acceleration.

The equation for Newton's second law of motion is

Where:

• = force, measured in newtons (N)

• = mass, measured in kilograms (kg)

• = acceleration, measured in metres per second squared (m s⁻²).

If a resultant force acts in the direction of motion of an object, then the object will speed up / accelerate in the direction of motion.

If a resultant force opposes the direction of motion of an object, then the object will slow down / decelerate.

If a resultant force acts at an angle to the direction of motion of an object, then the object will change direction.

True.

Acceleration does always act in the same direction as the resultant force.

True.

If no drag forces are present, then the acceleration of a falling object is independent of its mass. Astronauts on the Moon dropped a feather and a hammer from equal heights and found that they landed at the same time.

Newton's second law, in terms of momentum, states that the resultant force on an object is equal to its rate of change of momentum.

True.

Newton's first and second laws of motion can involve multiple forces acting on one object.

True.

Newton's third law of motion involves two objects exerting the same type of force on each other.

Newton's third law states that if one body (Object A) exerts a force on another body (Object B), the second body (Object B) will exert a force on the fist body (Object A) which is equal in magnitude but opposite in direction.

The four characteristics of a third law force pair are:

• the same type of force

• equal in magnitude

• opposite in direction

• acting on different objects

False.

Weight and normal contact force are not a third law pair because they:

• are not the same type of force

• act on the same object

False.

Two forces that are equal in magnitude and opposite in direction are not necessarily a third law force pair.

They must also be the same type of force, exerted by two different objects on each other.

Two examples of third law force pairs for a car driving at a constant velocity on a road are:

• normal contact forces due to the car pushing on the road and the road pushing back on the car

• weight due to the gravitational pull of the Earth on the car and the gravitational pull of the car on the Earth

A contact force is defined as a force that acts between objects that are physically touching.

Examples of contact forces are:

• surface friction

• fluid resistance / viscous drag

• tension

• normal reaction force

Surface friction is a force that opposes the motion of an object moving over a solid surface.

Viscous drag is a type of frictional force that occurs when an object moves through a fluid (a liquid or a gas).

Tension is a force that occurs within an object when a pulling force is applied to both ends.

The normal reaction force is the component of the contact force acting perpendicular to the surface.

Reaction forces act on objects supported by a surface.

In physics, a fluid is a liquid or a gas. The particles in a fluid are free to move around.

A non-contact force is a force which acts at a distance without any physical contact between bodies due to the action of a field.

Examples of non-contact forces are:

• gravitational force (weight)

• electrostatic force

• magnetic force

The gravitational force, or weight, is the attractive force experienced by two objects with mass in a gravitational field.

The electrostatic force is an attractive or repulsive force experienced by charged objects in an electric field.

The magnetic force is an attractive or repulsive force experienced between magnetic poles in a magnetic field.

False.

Air resistance is a type of fluid resistance or viscous drag caused by collisions with air particles. Therefore, air resistance is a contact force.

True.

When a frictional force is exerted on an object, energy is transferred.

False.

When a frictional force is exerted on an object, the temperature of the object increases because energy is transferred to the object by heating.

Surface friction is caused by imperfections in the surfaces of two objects that rub against one another.

Static friction is a type of surface friction that occurs when an object is stationary on a surface.

Dynamic friction is a type of surface friction that occurs when an object is moving across a surface.

True.

Surface friction always acts parallel to the plane of contact between the object and the surface.

False.

Static friction increases in magnitude until movement begins.

True.

For any given situation, static friction will reach a maximum value that is larger than that of dynamic friction.

True.

For a constant pushing force, dynamic friction will be constant. This is known as the coefficient of dynamic friction.

The equation for static friction is

Where:

• = frictional force, measured in newtons (N)

• = coefficient of static friction

• = normal reaction force, measured in newtons (N)

The equation for static friction is

Where:

• = frictional force, measured in newtons (N)

• = coefficient of dynamic friction

• = normal reaction force, measured in newtons (N)

A material obeys Hooke’s law if the extension of the material is directly proportional to the applied force up to the limit of proportionality.

The equation for Hooke's law is

Where:

• = elastic restoring force, measured in newtons (N)

• = spring constant, measured in newtons per metre (N m^–1)

• = extension, measured in metres (m)

The spring constant is a property of the material being stretched and describes the stiffness of the material.

False.

The stiffer the spring, the greater the spring constant.

True.

Hooke's law does apply to extensions and compressions.

The linear portion of a force-extension graph shows that the force applied is directly proportional to the extension, and so the material obeys Hooke's law.

The gradient of the linear region of a force-extension graph represents the spring constant, .

The gradient of the linear region of an extension-force graph represents .

Where:

• = spring constant, measured in newtons per metre (N m^–1)

The equation for Stokes' law is

Where:

• = viscous drag force, measured in newtons (N)

• = fluid viscosity, measured in newton seconds per metres squared (N s m^–2) or pascal seconds (Pa s)

• = radius of sphere, measured in metres (m)

• = velocity of sphere through fluid, measured in metres per second (m s^–1)

The viscosity of a fluid is its resistance to movement.

True.

The rate of flow of a fluid is inversely proportional to its coefficient of viscosity.

True.

The magnitude of the viscous drag force is dependent on the speed of the object moving through the fluid.

False.

The magnitude of the viscous drag force is dependent on the volume of the object moving through the fluid.

True.

The magnitude of the viscous drag force is dependent on the shape of the object moving through the fluid.

False.

The force of buoyancy is exerted on objects that are immersed in fluids (liquids and gases), not just liquids.

True.

The buoyancy force is exerted on a body due to the displacement of the fluid it is immersed in.

The equation for the buoyancy force is

Where:

• = buoyancy force, measured in newtons (N)

• = density of fluid, measured in kilograms per cubic metre (kg m^–3)

• = volume of the fluid displaced, measured in cubic metres (m^–3)

• = acceleration of free fall, measured in metres per second squared (m s^–2)

The weight of a sphere is

Where:

• = weight of sphere, measured in newtons (N)

• = density of sphere, measured in kilograms per cubic metre (kg m^–3)

• = volume of sphere, measured in cubic metres (m³)

• = acceleration of free fall, measured in metres per second squared (m s^–2)

False.

The terminal velocity of a sphere falling through a fluid is directly proportional to the square of the radius of the sphere.

False.

The terminal velocity of a sphere falling through a fluid is indirectly proportional to the viscosity of the fluid.

Linear momentum is the momentum of an object that is moving in only one dimension.

True.

The linear momentum of an object does remain constant unless the system is acted upon by an external resultant force.

The equation for linear momentum is

Where:

• = momentum, measured in kilogram metres per second (kg m s^–1)

• = mass, measured in kilograms (kg)

• = velocity, measured in metres per second (m s^–1)

True.

Linear momentum is a vector quantity with both magnitude and direction.

The principle of linear momentum states that the total linear momentum before a collision is equal to the total linear momentum after a collision. Unless the system is acted on by a resultant external force.

True.

Linear momentum is always conserved.

The linear momentum of a toy car of mass 0.2 kg that travels with a velocity of 0.1 m s^–1 is 0.02 kg m s^–1 .

The equations for the momentum before and after a collision between moving object A and stationary object B are:

Impulse is when an external resultant force acts on an object for a very short time and changes the object's motion.

The symbol for impulse is .

The equation for the impulse of a force is

Where:

• = impulse, measured in newton seconds (N s)

• = resultant external force applied, measured in newtons (N)

• = change in time over which the force acts, measured in seconds (s)

True.

Impulse is equal to change in momentum. Therefore, change in momentum can be used to indirectly measure impulse.

False.

Impulse always acts in the same direction as the external resultant force.

True.

A larger force exerted for a short time has the same effect as a smaller force exerted for a longer time.

True.

Increasing the time over which a change in momentum occurs reduces the force experienced by the object.

The impulse of the force is .

Impulse is the area under a force-time graph, therefore:

False.

The equation can also be used when the mass of the object is not constant.

The force exerted by the skirting board on the car is –4.5 N.

According to Newton's third law:

• the car exerts a force of 4.5 N on the skirting board

• therefore, the skirting board exerts an equal and opposite force of -4.5 N on the car

The magnitude of the force exerted by the chair on the student is 490 N.

The student exerts a normal reaction force on the chair that is equal to the student's weight.

According to Newton's third law, the chair exerts a normal reaction force on the student that is equal in magnitude but opposite in direction.

False.

The equation can only be used when mass is constant.

Force, as the rate of change of momentum, be derived from Newton's second law of motion as follows:

A collision is when two or more moving objects come together and exert a force on one another for a relatively short time.

An explosion is when two or more objects that are initially at rest, are propelled apart from one another.

True.

Momentum is always conserved in collisions and explosions.

False.

Kinetic energy is only conserved in elastic collisions and explosions.

However, kinetic energy is not conserved if the collision or explosion is inelastic.

An elastic collision is a collision in which both the momentum and kinetic energy are conserved.

An inelastic collision is a collision in which the momentum is conserved but the kinetic energy is not.

True.

Perfectly elastic collisions only occur between particles. However, the theoretical idea of an elastic collision can be used in exam questions.

To determine whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision. If kinetic energy is conserved, then the collision is elastic.

False.

A totally inelastic collision is a special case of an inelastic collision where the colliding bodies stick together and move as one body.

A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

A complete circle is radians.

The equation used to convert degrees to radians is .

A half circle is radians.

The equation used to convert radians to degrees is .

90° is radians.

Angular displacement is the change in angle, in radians, of a body as it rotates around a circle.

270° is radians.

Angular speed is the change in angular displacement with respect to time.

Angular speed is a scalar quantity, and angular velocity is a vector quantity. Angular speed is the magnitude of angular velocity.

The equation linking linear speed, and angular speed is

Where:

• = linear speed, measured in metres per second (m s^–1)

• = radius of circle, measured in metres (m)

• = angular speed, measured in radians per second (rad s^–1)

The equation linking linear speed, and angular speed is

Where:

• = linear speed, measured in metres per second (m s^–1)

• = time period, measured in seconds (s)

Centripetal means acting toward the centre of the circular path.

True.

An object in uniform circular motion travels at a constant speed but with a changing velocity. Velocity is a vector quantity, so a change in direction is a change in velocity.

Centripetal force is defined as the resultant force required to keep a body in a uniform circular motion that acts towards the centre of the circle, perpendicular to the velocity.

The equation linking centripetal force and linear speed is

Where:

• = centripetal force, measured in newtons (N)

• = mass, measured in kilograms (kg)

• = linear speed, measured in metres per second (m s^–1)

• = radius of orbit, measured in metres (m)

The equation linking centripetal force and linear speed is

Where:

• = centripetal force, measured in newtons (N)

• = mass, measured in kilograms (kg)

• = radius of orbit, measured in metres (m)

• = angular speed, measured in radians per second (rad s^–1)

True.

The direction of the centripetal force is the same direction as the acceleration. Centripetal force is a resultant force. Acceleration always occurs in the direction of the resultant force.

The centripetal force for the Earth orbiting the Sun is the gravitational force.

The centripetal force for a ball on a rope moving in a circle is tension.

The centripetal force for a car going around a circular track is friction.

True.

For an object in circular motion, there is no work done because there is no change in kinetic energy.

The equation linking centripetal acceleration and linear speed is

Where:

• = centripetal acceleration, measured in metres per second squared (m s^–2)

• = linear speed, measured in metres per second (m s^–1)

• = radius of circular orbit, measured in metres (m)

Centripetal acceleration is the acceleration of an object towards the centre of a circle when an object is in circular motion at a constant speed.

The equation linking centripetal acceleration and linear speed is

Where:

• = centripetal acceleration, measured in metres per second squared (m s^–2)

• = angular speed, measured in radians per second (rad s^–1)

• = radius of circular orbit, measured in metres (m)

True.

Centripetal acceleration is in the same direction as the centripetal force. Centripetal force is a resultant force, acceleration always acts in the same direction as the resultant force.

The equation linking centripetal acceleration and time period is

Where:

• = centripetal acceleration, measured in metres per second squared (m s^–2)

• = radius of circular orbit, measured in metres (m)

• = time period, measured in seconds (s)

Non-uniform circular motion occurs when there is a changing resultant force on an object in circular motion, such as when an object moves in a vertical circle.

Examples of objects in non-uniform circular motion are:

• a ball swinging on a string in a vertical circle

• swinging a bucket of water in a vertical circle

False.

For a ball on a string swinging in a vertical circle, the tension force of the string on the ball is greater at the bottom of the circle than at the top. This is because the tension has to overcome the weight force at the bottom of the circle.

True.

For a ball on a string swinging in a vertical circle, the direction of the tension force will change continually. This is because tension is the centripetal force and is always directed to the centre of the circle.

False.

For a ball on a string swinging in a vertical circle, the magnitude of the tension force will change continuously. This is because tension is the centripetal force, which is greater at the bottom because it also has to overcome the weight force at the bottom of the circle.

For an object in non-uniform circular motion, the centripetal force is at a maximum at the bottom of the circle and a minimum at the top of the circle.

The equation for the centripetal force on a ball swinging in a vertical circle when the ball is at the top of the circle is

Where:

• = centripetal force / tension measured in newtons (N)

• = mass, measured in kilograms (kg)

• = velocity, measured in metres per second (m s^–1)

• = radius of orbit, measured in metres (m)

• = gravitational field strength, measured in newtons per kilogram (N kg^–1)

The equation for the centripetal force on a ball swinging in a vertical circle when the ball is at the bottom of the circle is

Where:

• = centripetal force / tension, measured in newtons (N)

• = mass, measured in kilograms (kg)

• = velocity, measured in metres per second (m s^–1)

• = radius or orbit, measured in metres (m)

• = gravitational field strength, measured in newtons per kilogram (N kg^–1)

False.

For a ball on a string swinging in a vertical circle, the speed of the ball will be faster at the bottom of the circle than at the top, because the acceleration is greater at the bottom.