A cart of mass rests on a nearly frictionless horizontal air track
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A cart of mass 6.0kg rests on a nearly frictionless horizontal air track. Two horizontal forces act on the cart simultaneously and remain constant in time.
• Force F1 has magnitude 5.0N and points 35∘ above the +x–axis.
• Force F2 has magnitude 5.0N and points 35∘ below the +x–axis.
Assume no other horizontal forces act on the cart during the time interval considered, and air resistance is negligible.
(a) Draw a clearly labeled free-body diagram for the cart that shows all forces acting on it.
(b) Without performing any trigonometric calculations, determine the direction of the net force on the cart. Justify your answer using properties of vector components.
(c) Compare the magnitude of the cart’s acceleration when both forces act to the magnitude of the acceleration that would result if only F1 acted alone. Provide a qualitative explanation based on Newton’s second law.
(d) Suppose instead that the magnitude of F2 were greater than that of F1, while their directions remained the same. Explain qualitatively how this change would affect the direction of the cart’s acceleration.