Newton's second law questions in the Mechanics paper usually involve connected particles, pulleys, slopes, or a car with a trailer. The method is straightforward but the equations are easy to get wrong. This guide collects what Cambridge examiners say students get wrong, based on recent reports.
Summarised in our own words from a reading of the examiner reports.
Mistakes that cost marks
- Missing terms. The most repeated problem. Students omitted a force, often the resistance, the weight, or the component of the weight on a slope. Some did not include g in the weight component or the friction term. One report notes that several students forgot to include g when finding the weight component, and another that some included a component of an applied force that did not belong.
- Signs. Sign errors in the equation of motion were common, such as a single sign error giving a = −6.07, or the incorrect T − 0.6g = 0.6a for particle A when it was moving down.
- Equations for the system. When the system equation is used, the forces were equated to the mass of one particle (0.4a) instead of the total mass ((0.4 + 0.7)a).
- Tension. Students assumed the tension was the same as in an earlier part when the situation had changed, or did not consider the effect of the tension at all, or left tension out of an equation for a single particle. In a car and trailer question, the force in the tow-bar does not appear in the equation for the whole system, though it does for each part.
- Connected particles. A very common misconception was to assume two connected particles had different speeds, forgetting that they have the same speed while the string is taut.
- Using the wrong velocity. Students used the speed with which a particle was projected, not the speed just before a collision, or assumed both decelerations were equal when the friction and the weight component both acted against the motion.
- Wrong direction of friction. The frictional force in the wrong direction, or the tension from an earlier part used when the friction was reversed.
- Using the wrong approach to the work done. Some students multiplied the pulling force by the distance when the force was at an angle, or used the wrong component of the force.
- Not following through. Students with wrong values for acceleration or tension in an earlier part could still earn marks if they followed through, but few did, as one or more terms were often omitted.
- Pairs of equations. Errors were commonly seen in finding the acceleration of the second particle.
What examiners advise
- Apply Newton's second law to each particle separately, or to the system, but do not mix the two.
- Draw a force diagram for each body. One report says the diagram should show that the tension and the weight component for one particle act in the same direction.
- Check each equation for missing or extra terms and for the component of weight on a slope.
- Write the acceleration with a sign that matches the direction of motion.
- State the assumption that the string is taut or inextensible when you say that two particles have the same speed or acceleration.
Habits that help
- Write "F = ma" and the direction of positive motion at the top of each equation.
- Put the forces on the left and mass times acceleration on the right, with the resultant forces in the direction of the acceleration.
- Check that your answer for acceleration makes sense for the situation, such as a positive acceleration for a particle that is speeding up.
Questions students ask
Why do my Newton's second law equations lose marks?
Missing terms are the most repeated problem. Students omit a force, often the resistance, the weight, or the weight component on a slope, or leave out g. Check each equation for missing or extra terms and for signs.
How do I handle connected particles?
Apply Newton's second law to each particle separately, or to the system, but do not mix the two. For the system, use the total mass: (0.4 + 0.7)a, not 0.4a. Two connected particles have the same speed and acceleration while the string is taut.
Is the tension the same in every part of the question?
No. Students assumed the tension was unchanged from an earlier part when the situation had changed, or left it out of the equation for a single particle.
Which way does friction act?
Against the motion. Reports record friction in the wrong direction and tension from an earlier part used when friction was reversed.
What if I got a wrong acceleration in an earlier part?
You can still earn marks by following through, but few students did, because one or more terms were often omitted.
Practice this topic
Ready to try some? Work through past paper questions on this topic one at a time. Attempt each question fully first, and open the mark scheme only afterwards.