Newton's laws of motion Simulations | AS & A Level Mathematics 9709

1 interactive lab · AS & A Level Mathematics 9709

Connected Particles: Pulleys and Towing

4.4 Newton's laws of motion · Predict whether two particles on a string over a pulley, or a car towing a trailer, move; then write F = ma for each and eliminate T to find a and T.

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About this lab

Predict whether two particles on a string over a pulley, or a car towing a trailer, move; then write F = ma for each and eliminate T to find a and T.

You will be able to

Draw the forces on each of two connected particles and write Newton's second law F = ma separately for each, with the tension the same on both sides of a smooth pulley.
Calculate the acceleration and the tension by eliminating T for a particle on a smooth or rough horizontal or inclined plane, joined by a light inextensible string to a hanging particle (g = 10 m s⁻²).
Determine whether the particles move or are held by friction by comparing the friction needed with μR, and state which way they move.
Calculate the acceleration of a car towing a trailer and the force in the rope or tow-bar, and explain what a negative value of T (a thrust) means.

Examiner's note. Draw a force diagram for each particle and write F = ma separately for each (resultant force in the direction of the acceleration) with every number substituted. The tension T is the same on both sides because the string is light and the pulley is smooth, and both particles have the same acceleration because the string is inextensible: add the two equations to eliminate T, then substitute back to find it. On a slope use R = mg cos α and friction F = μR only when the particles are moving (or about to); decide the direction of motion first, and check whether friction could hold them (friction needed ≤ μR). A tow-bar can carry a thrust (T negative), a rope cannot. The classic slips are T = mg for a hanging particle that is accelerating, leaving out the weight component mg sin α, and friction acting the wrong way.

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Newton's laws of motion