Forces and Force Diagrams
This topic covers the fundamental concept of forces in mechanics. It involves identifying various types of forces, understanding what affects their size and direction, and combining them to find the overall 'resultant force' which dictates an object's motion.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- Forces are vector quantities, meaning they have both a magnitude (size, in Newtons) and a direction.
- Forces can be categorised as contact (e.g., friction, tension, normal contact) or non-contact (e.g., weight, electrostatic, magnetic).
- A force diagram illustrates all forces acting *on* a single object. Each force is an arrow starting on the object and pointing in the correct direction.
- The resultant force is the vector sum of all forces acting on an object. It is not an additional force and should never be drawn on a force diagram.
- If the resultant force is zero, the object's velocity is constant (which includes being at rest). If the resultant force is non-zero, the object accelerates.
- Weight acts downwards towards the centre of the gravitational field, while drag and friction always act to oppose relative motion.
Diagrams
› Why does this happen?
Why draw forces only *on* one object?
A force diagram is used to predict how one specific object will move. Newton's laws connect the forces acting *on* an object to the acceleration *of that same object*. That's why we must isolate it. For example, when you push a box, the box pushes back on your hand. The force on the box affects its motion. The force on your hand affects *your* motion. If you drew both on one diagram, you wouldn't be able to work out the box's acceleration. A force diagram for the box must only show forces acting *on the box*.
Why is the resultant force never drawn on a force diagram?
The resultant force isn't a separate, physical force. It's the *overall effect* or the vector sum of all the real forces already drawn (like pushes, pulls, weight, and friction). Drawing it on the diagram would be like counting the forces twice. If a 10 N push is opposed by 4 N of friction, the resultant force is 6 N. The 6 N is simply the outcome of the 10 N and 4 N forces competing; it's not a third force being applied to the box.
Where do drag and friction come from?
These forces oppose motion because of interactions between surfaces or with particles. Drag (or air resistance) is caused by an object colliding with and pushing air particles out of the way. Every particle it hits pushes back a small amount. The total force from billions of these tiny pushes is what we call drag. Friction is similar, but it happens between solid surfaces. It's caused by microscopic roughness, where tiny bumps and ridges on the surfaces catch and resist sliding past each other.
Formulae
W = m g To calculate the weight (W) of an object from its mass (m) and the gravitational field strength (g).
Fresultant = Fforward - Fbackward To calculate the resultant force in one dimension by defining a positive direction (e.g., 'forward') and subtracting the sum of forces in the opposite direction.
Definitions
- Resultant Force
- The single force that has the same effect as all the individual forces acting on an object combined. It is the vector sum of all forces.
- Normal Contact Force
- A repulsive force that acts perpendicular (normal) to a surface when an object is in contact with it, preventing the object from passing through the surface.
- Friction
- A resistive force that opposes the relative sliding motion or attempted motion between two solid surfaces in contact.
- Upthrust
- An upward force exerted by a fluid (liquid or gas) that opposes the weight of an object partially or fully immersed in it. It is equal to the weight of the fluid displaced by the object.
- Tension
- A pulling force transmitted axially by means of a string, cable, chain, or similar object. It acts along the length of the object.
Worked example
A small crate of mass 5 kg is sliding down a rough slope. At one instant, the gravitational force component pulling it down the slope is 25 N. Friction provides a constant resistance of 4 N, and air resistance provides a further 1 N of drag. What is the magnitude of the resultant force on the crate down the slope?
- 1
Identify the forces acting along the slope.
The driving force is the component of gravity, acting down the slope.
The resistive forces are friction and air resistance, both acting up the slope.
- 2
Assign a positive direction.
Let's define 'down the slope' as the positive direction.
- 3
Sum the forces in the positive direction:
Fdown = 25 N - 4
Sum the forces in the negative direction (up the slope):
Fup = Friction + Air Resistance = 4 N + 1 N = 5 N - 5
Calculate the resultant force:
Fresultant = Fdown - Fup - 6
Substitute the values:
Fresultant = 25 N - 5 N = 20 N - 7
The resultant force is 20 N in the positive direction, which is down the slope.
Answer: 20 N
Common mistakes
- ×Sign errors: When calculating the resultant force, forgetting to subtract the forces acting in the opposite direction. Always define a positive direction and stick to it.
- ×Confusing mass and weight: Using mass (in kg) in a force calculation instead of weight (in N). Remember to calculate weight using W = mg first.
- ×Missing forces: Overlooking a force mentioned in the problem description, like friction or air resistance, when summing the forces.
- ×Diagram errors: Drawing the resultant force as if it were a real, separate force acting on the object. It is the net effect, not an applied force.
No-calculator tips
- ✓Assume g = 10 m/s2 or 10 N/kg unless specified otherwise. This turns weight calculations into simple multiplication.
- ✓Before performing the final calculation for resultant force, mentally group all forces acting in one direction and all forces in the other. This reduces the problem to a single subtraction.
- ✓If a force diagram is provided, quickly redraw a simplified version, labelling forces with their numerical values to avoid misreading the diagram mid-calculation.