Kinematics and Newton's laws · Cinemática y leyes de Newton
| English | Español |
|---|---|
| resultant force/rɪˈzʌltənt fɔːs/ | fuerza resultante |
Which force accelerates the trolley?
- A trolley accelerates while friction opposes its motion. The engine's force alone does not equal mass times acceleration.
- This lesson studies resultant force 合力: The vector sum of all external forces acting on the modelled object.
Choose the mathematical structure
- Choose a positive direction and draw a force diagram. Use resultant F=ma. For constant acceleration, v=u+at and s=ut+at²/2. A particle model ignores size; a smooth surface ignores friction.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines resultant force? · ¿Qué descripción define correctamente la fuerza resultante?
The vector sum of all external forces acting on the modelled object. · La suma vectorial de todas las fuerzas externas que actúan sobre el objeto modelado.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
A 5 kg trolley has driving force 18 N and resistance 3 N. The resultant is 15 N, so a=15/5=3 m/s². Starting from rest for 4 s gives v=0+3×4=12 m/s and s=0×4+3×4²/2=24 m.
Kinematics and Newton's laws · Cinemática y leyes de Newton
Choose a positive direction and draw a force diagram · Elige una dirección positiva y dibuja un diagrama de fuerzas
Compare the model with the worked case and explain one change. · Compara el modelo con el caso resuelto y explica un cambio.
Find acceleration for mass 5 kg and resultant force 15 N. · Encontrar la aceleración para una masa de 5 kg y una fuerza resultante de 15 N.
Use the resultant: a=F/m=15/5=3. · Usar la resultante: a=F/m=15/5=3.
Test a tempting shortcut
- The normal reaction need not equal weight on a slope. Connected-particle models need one equation per particle and a consistent acceleration relation. The constant-acceleration formulae cannot be used for arbitrary variable acceleration.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The constant-acceleration formulae apply unchanged when acceleration varies with time. This claim is false. Explain which definition or assumption it violates.
Starting from rest at a=3 m/s², find speed after 4 s. · Partiendo del reposo con a=3 m/s², encontrar la velocidad después de 4 s.
v=u+at=0+3×4=12.
The constant-acceleration formulae apply unchanged when acceleration varies with time. · Las fórmulas de aceleración constante se aplican sin cambios cuando la aceleración varía con el tiempo.
The normal reaction need not equal weight on a slope. Connected-particle models need one equation per particle and a consistent acceleration relation. The constant-acceleration formulae cannot be used for arbitrary variable acceleration. · La reacción normal no tiene que ser igual al peso en una pendiente. Los modelos de partículas conectadas requieren una ecuación por partícula y una relación de aceleración consistente. Las fórmulas de aceleración constante no pueden usarse para una aceleración variable arbitraria.
Interpret a new situation
- Explain what each idealisation permits and what it leaves out. For a velocity-time graph, gradient represents acceleration and signed area represents displacement.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
For that motion, find displacement after 4 s. · Para ese movimiento, encontrar el desplazamiento después de 4 s.
s=ut+at²/2=0+3×16/2=24.
Match each part of a complete solution to its purpose. · Emparejar cada parte de una solución completa con su propósito.
An assumption justifies the model; a check tests the result; interpretation connects it to the question. · Una suposición justifica el modelo; una comprobación verifica el resultado; la interpretación lo conecta con la pregunta.
Use this in your course
- edexcel IAL further mathematics; official unit M2. Other-unit enrichment is identified in the scope review; it is not an extra cash-in requirement.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The vector sum of all external forces acting on the modelled object. Choose the relationship, show the method, check its assumptions and interpret the result.