PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Three carts A, B, and C of masses 2.0kg, 1.5kg, and 3.5kg, respectively, are lined up in that order on a horizontal track. The carts are connected by light, inextensible strings, and a horizontal force of constant magnitude 12N is applied to cart A toward the right.
Assume the strings remain taut at all times and the carts start from rest.
Answer the following questions, showing all work and clearly stating any assumptions you make.
(a) Determine the magnitude of the acceleration of the system while the track is frictionless.
(b) Calculate the magnitude of the tension TAB in the string between carts A and B and the tension TBC in the string between carts B and C under the same frictionless conditions.
(c) The track is now coated with a material that gives each cart a coefficient of kinetic friction μk=0.15. Compute the new magnitude of the acceleration.
(d) For the case with friction in part (c), determine the new values of TAB and TBC.
(e) A student claims that the tensions inside the strings cannot affect the acceleration of the three–cart assembly. Using Newton’s laws, justify or refute this claim in one or two well-reasoned paragraphs.