Only two horizontal forces act on a 3.0 kg body. One force is 9.0 N, acting due east, and the o

Only two horizontal forces act on a 3.0 kg body. One force...

Only two horizontal forces act on a 3.0 kg body. One force is $9.0 \mathrm{~N}$, acting due east, and the other is $8.0 \mathrm{~N}$, acting $62^{\circ}$ north of west. What is the magnitude of the body's acceleration?

Key Concepts

Vector Addition

Vector addition is the method of combining multiple vectors to determine a net or resultant vector. By adding corresponding components of individual forces, one can compute the overall effect on an object's motion.

Newton’s Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is used to relate the net force obtained from vector addition to the acceleration experienced by the object.

Force Vectors

Force vectors represent forces as quantities having both magnitude and direction. They are essential for analyzing the effects on an object when multiple forces act simultaneously, providing the basis for calculating net effects in the form of a resultant force.

Vector Decomposition

Vector decomposition involves breaking a vector into its horizontal and vertical components. This process simplifies the analysis of forces by allowing separate treatment of motion in perpendicular directions, making it easier to calculate contributions from each force.

Transcript

00:01 This is not given that only two hodg gentle forces acting on the 3 kggbils right so basically mass is given 3 kgg and forces acting on the body is 9 newton acting due to east so since let's say this is body and this is east so 9 newton and other each a 672 degree with the north of west north of west okay so since this is west so this is north and this is this is north as in south so north of west that means the 72 degree with the best and in between the north okay so this will be best so what will be the component of course then and this force is given as a out mutant okay so aught neuron so this component will be nothing but out of cost 60 out of cost 62 degree okay so what will be the acceleration in this direction so net force will be nothing what 9 minus of 8 of cos of 62 degree so that means acceleration a will nothing what f upon m so 9 minus of 8 of course 62 degree so 8 of course 62 degree that will be 3 .75 and the multiplication of 3 .75 upon the mass is 3kg it comes out to be it comes out to be 1 .78 1 .78 acceleration a comes out to be 1 .7 8 meter per second as and in which direction in extra direction and there will be one more acceleration in which direction and the force will force if this component will be in this reaction that is f of sign of 62 degree so what will be the value of that so a x this is a y it will be nothing but f of sign f f f f f f f y upon mass so f y is nothing but eight into sign of 62 degree upon mass 3 so the sign of 62 degree you need to point sign of 62 degree right so 8 .8 it comes out to be 8 .8 0 .08 into 8 and divided by 3.

02:07 So it comes out to be fy.

02:11 Yeah, so ay comes out to be 2 .35.

02:15 Okay, so the net acceleration values, these are the particular ventricular, so a net having magnitude equal to a x square, plus a y, that means 1 .78 square and plus of 2 .35 square.

02:30 Okay, so now we need to find this value.

02:32 So 1 .78 square, and plus of 2 .35 into 2 .35...

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