A block of mass 2.0 kg rests on a nearly frictionless horizontal surface
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A block of mass 2.0 kg rests on a nearly frictionless horizontal surface. Three horizontal forces act simultaneously on the block:
• F1=5.0N directed 0° (due east)
• F2=8.0N directed 120° (measured counter-clockwise from east)
• F3=4.0N directed 225°
Angles are given in the standard mathematical sense: 0° along +x (east), 90° along +y (north), etc.
(a) Determine the x-component and y-component of each force, then calculate the resultant force acting on the block. Give the magnitude and direction of the resultant.
(b) Using your result from part (a), compute the block’s acceleration vector.
(c) An engineer wants the block to accelerate strictly north with a magnitude of 2.0 m s⁻². Determine the magnitude and direction of a single additional horizontal force that would have to be applied to achieve this motion.
(d) Justify, using component reasoning, that the force you calculated in part (c) will indeed cause the required purely northward acceleration.