# Forces and Newton's Laws

**AS Level**

- Understand the concept of a force; understand and use Newton’s first law
- Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors
- Understand and use weight and motion in a straight line under gravity; gravitational acceleration, g, and its value in S.I. units to varying degrees of accuracy
- (The inverse square law for gravitation is not required and g may be assumed to be constant, but students should be aware that g is not a universal constant but depends on location)
- Understand and use Newton’s third law; equilibrium of forces on a particle and motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); application to problems involving smooth pulleys and connected particles

**A Level**

- extend to situations where forces need to be resolved (restricted to 2 dimensions)
- resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces
- Understand and use addition of forces; resultant forces; dynamics for motion in a plane
- Understand and use the F≤μR model for friction; coefficient of friction; motion of a body on a rough surface; limiting friction and statics

## Links and Resources

### Forces in 1 Dimension

This simulation from the University of Colorado can show force, acceleration, position and velocity graphs for motion in 1 dimension. Force, mass and friction can all be altered in the simulation and any or all the graphs displayed.

### F=ma in a Helicopter

This activity provides examples and ideas for students investigating what happens to packages hanging below a helicopter. The lesson plan describes a lesson activity designed to promote discussion about what happens when the helicopter is accelerating, moving with constant velocity and decelerating. The students then model the situation mathematically. The teaching notes include teaching tips and how the resources could be adapted.

### Projectile Motion

A simulation by The University of Colorado.

### Mechanics 1

This Nuffield Advanced Mathematics text book has comprehensive teaching material and sets of questions.

Unit 1 deals with motion in one dimension and projectiles.

Unit 2 deals with forces including weight and friction. Forces are resolved and shown as line segments in force diagrams or as column vectors.

### Vectors - Motion and Forces in Two dimensions

This is a link to The Physics Classroom.

Lessons 1 and 3 deal with vectors and applications to force and velocity. Topics covered include, resolving vectors into perpendicular components, addition of vectors, equilibrium and statics, bodies on an inclined plane and simple examples of relative velocity.

Lesson 2 deals with projectile motion under gravity.

### Monkey and Hunter

This short video illustrates the independence of perpendicular vectors. A projectile fired horizontally towards an object is shown to hit the object if they fall from the same height at the same time.

### Projectiles

This series of interactive excel sheets look at projectiles, either on or above the horizontal plane.

The first sheet defines the symbols and units used in the remaining sheets. Other sheets allow the angle of projection and initial velocity to be altered and the range, maximum height and time of flight to be calculated.

The last sheet contains questions on five different projectiles for students to complete a table be entering the missing values. Answers can be revealed and a new set of questions can be generated each time.

### Inclined Plane

This series of interactive excel sheets investigate models involving an inclined plane.

The first sheet helps students to investigate the conditions for movement of an object on a horizontal plane. The subsequent sheets deal with models on an inclined plane where initially there is no friction then the coefficient of friction is introduced.

The fourth sheet shows a mass at rest on an inclined plane. By adjusting the variables the acceleration of the ensuing downward motion can be investigated. The next sheet looks at a similar model, this time however an external force parallel to the plane is applied to the mass.

The final model again shows a mass in equilibrium on an inclined plane, however this time it is subject to a horizontal external force. Values can be adjusted which see the mass slide up the plane.

### Statics: Forces at a Point

This series of interactive excel sheets look at systems in static equilibrium.

The first sheet looks at two forces acting on a point in which the angle and value of either one of the two forces, or resultant force, are to be found. The next sheet repeats the process for three forces acting at a point.

The third sheets shows three forces acting on a point. Their components parallel to each axis and the resultant force are shown.

The fifth interactive sheet shows an object in equilibrium on an inclined plane under the action of three forces.

The final sheet contains a series of six questions in which students have to find the magnitude and direction of the resultant force when given three forces acting on a point. In the second set of questions i and j notation is used.

### Forces In Strings

This series of interactive excel sheets look the forces within strings.

The first sheet shows an adjustable mass hanging on an inextensible string, and demonstrates the fact that the tension is equal to the weight.

The second sheet shows the tension on an inextensible string when a horizontal force is applied to a mass of 0.25kg. The horizontal force and the angle between the string and the vertical plane can both be adjusted.

The third sheet illustrates a mass supported by two inextensible strings.

The fourth sheet looks at a mass held in equilibrium on an inclined plane. The angle of the plane and the mass of the weight can be adjusted and the corresponding normal reaction and tension forces can be shown.

### Mechanics in Action

This textbook is for teachers who wish to explore the use of practical investigations in mechanics.

Chapter 5 (from pdf page 66) provides ideas for investigating forces including forces acting on particles connected by pulleys.

Chapter 7 (from pdf page 94) deals with friction and also includes connected particles and pulleys.

Subject(s) | Mathematics |
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Tags | A level mathematics |

Age | 16-19, FE/HE |

Last updated | 07 March 2017 |

Rating | |

URL | https://www.stem.org.uk/lxaqdt |

Comments | 0 |