Lesson summary
3.1.4 Force and Momentum — AS PHYSICS 9702 notes: Express Newton's second law as rate of change of momentum and use impulse to explain impact forces.Force = the rate of change of momentum: F = Δp ÷ Δt.What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = chan…
- Δp = pfinal − pinitial
- For constant mass Δp = mΔv
- The momentum form is more general
- Impulse equals the change in momentum
- For a varying force
- The average force
Section 1 of 10Second law in momentum form
Second law in momentum form
Force
Force the rate of change of momentum: F = Δp ÷ Δt.
What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
The resultant force acts in the direction of the change in momentum.
Δp
Δp pfinal − pinitial
- force and momentum are vectors, so the sign shows direction.
For constant mass Δp = mΔv
- For constant mass Δp = mΔv so F = ma.
The momentum form is more general
- The momentum form is more general it works when mass changes, such as a rocket burning fuel, and for collisions with varying force.
Section 2 of 10Impulse
Impulse
Impulse
Impulse force × time: FΔt = Δp.
Impulse equals the change in momentum
- Impulse equals the change in momentum with unit N s = kg m s-1.
For a varying force
- For a varying force the impulse is the area under the force-time graph.
The average force
The average force impulse ÷ contact time.
The gradient of a momentum-time graph
- The gradient of a momentum-time graph is the force.
Section 3 of 10Time of impact
1For a given change in momentum
- For a given change in momentum the force is inversely proportional to the time taken.
2As Δt increases F decreases
- As Δt increases F decreases and as Δt decreases F increases.
3Longer time reduces force
- Longer time reduces force catching a ball by drawing the hands back, crumple zones, seat belts, airbags, padded helmets, landing mats and bending the knees.
4Shorter time gives a large force
- Shorter time gives a large force as with a golf club or tennis racket in brief contact.
Section 4 of 10Direction of forces in an impact
Direction of forces in an impact
The force on an object is negative
- The force on an object is negative if it opposes the direction of the initial velocity.
The force the wall exerts on a car equals the force the car exerts on the wall
- The force the wall exerts on a car equals the force the car exerts on the wall equal in magnitude and opposite in direction, Fcar = −Fwall.
In a rebound take the final velocity as negative
- In a rebound take the final velocity as negative so the change in momentum is larger.
Section 5 of 10Streams of fluid
Streams of fluid
For a continuous stream such as water or hail
- F = (Δm ÷ Δt)Δv.
A jet of water that stops completely on a wall
- F = v(Δm ÷ Δt).
If it bounces back with the same speed
- If it bounces back with the same speed the force is double.
Section 6 of 10Variable forces and graphs
Variable forces and graphs
During a bat striking a ball the force-time graph
- During a bat striking a ball the force-time graph rises to a peak and falls.
The impulse is the area under the graph
- The impulse is the area under the graph found by counting squares or splitting into triangles and rectangles.
The peak force is larger than the average force
- The peak force is larger than the average force for a triangular pulse the peak is twice the average.
Contact times are milliseconds
- Contact times are milliseconds so forces can be large even for modest changes in momentum.
A data logger with a force sensor
- A data logger with a force sensor records the pulse and gives the area directly.
Section 7 of 10Links to other ideas
Links to other ideas
The momentum form links the kinematic equations to collisions.
Newton's third law in a collision
- Newton's third law in a collision the forces are equal and opposite for the same time, so the impulses are equal and opposite.
The changes of momentum cancel
- The changes of momentum cancel which is the basis of the conservation of momentum.
Section 8 of 10More from the specification
More from the specification
Gravitational acceleration on planetary surfaces
- Gravitational acceleration on planetary surfaces gravitational field strength determines local acceleration due to gravity,
- making object weight vary between Earth and Moon.
Newton's second law and resultant force
- Newton's second law and resultant force unbalanced resultant forces acting on an object produce acceleration proportional to force and inversely proportional to mass.
Unit conversion in momentum calculations
- Unit conversion in momentum calculations converting vehicle velocities from kilometres per hour to metres per second ensures consistent SI momentum calculations.
Newton's Second Law and Linear Momentum
- The resultant force acting on a body equals the time rate of change of its linear momentum;
- (Fnet = Δp / Δt)
- when mass remains constant, this simplifies to Fnet = m·a,
- where a is the resulting acceleration in the direction of motion.
Gravitational Force and Weight
- The downward weight of an object near the Earth's surface represents the gravitational attractive force exerted on it (W = m·g);
- when drag forces equal weight, vertical forces become balanced and acceleration ceases.
Impulse and Impact Collisions
- When a moving projectile or sports ball strikes a surface, the impulse of the impact force equals the change in momentum (F·Δt = Δp);
- calculating this permits engineers to determine peak collision forces.
Vector quantity
- A quantity with both magnitude and direction.
Solar system
- A star with the objects that orbit it.
Acceleration
- Rate of change of velocity.
Weight
- Gravitational force on a mass.
Balanced
- Having equal and opposite moments.
Linear
- A graph that is a straight line through the origin, so resistance is constant.
W = mg
What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg−1 on Earth)
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Impulse | Force multiplied by the time for which it acts, equal to the change in momentum. |
| Rate of change of momentum | Change in momentum divided by the time taken, equal to the resultant force. |
| Contact time | The time during which two objects are in contact in a collision. |
| Average force | The impulse divided by the contact time. |
| Force-time graph | A graph whose area is the impulse. |
| Newton's third law | Two interacting bodies exert equal and opposite forces on each other. |
| Mass flow rate | The mass of fluid per second reaching a surface, Δm ÷ Δt. |
| Rebound | Motion back in the opposite direction after a collision. |
Section 10 of 10Exam technique
1
Using F = ma when the mass changes — use F = Δp ÷ Δt.
2
Not reversing the sign of velocity for rebounds, so Δp is too small.
3
Mixing up impulse (N s) with energy (N m).
4
Reading the area under a force-time graph with time in the wrong units — use seconds.