Two workers pull a heavy crate of mass across a level warehouse floor where kinetic…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
Two workers pull a heavy crate of mass 20kg across a level warehouse floor where kinetic friction is negligible. Worker A pulls with a constant horizontal force of magnitude 40N toward the east. Worker B pulls with a rope of the same length attached to the crate at the same point but at an adjustable angle θ north of east, exerting a constant force of magnitude 50N. The goal is to have the crate accelerate directly toward the east (with no north–south component of acceleration).
(a) Show that the condition for zero north–south component of acceleration can be written as 50sinθ=0. Clearly state any assumptions used.
(b) Determine the numerical value of θ that satisfies the condition found in part (a).
(c) Using the value of θ from part (b), calculate the magnitude of the crate’s eastward acceleration.
(d) Explain why the angle found in part (b) is independent of the mass of the crate as long as the workers’ applied forces remain the same.