A 10 N force acts due North on a 2 kg object while a 15 N force acts due East on the object. The acceleration of the object is then ________m/s2.

Answer 1

Hi again Nilufar

Here it will be useful to keep units in mind. The units of force are kilogram meters per second square (or mass times acceleration). Therefore for the units to come out right, the acceleration of the object will be equal to the net force acting on it divided by its mass and will point in the direction of the net force.

To find the net force, we need to know how multiple forces in different directions combine. Luckily they combine very simply, with forces in opposite directions canceling out and forces in the same direction adding. Forces in perpendicular directions are independent components of the net force. In our case we have two perpendicular forces. The 10 Newtons of force pushing north will cause a northward acceleration of 5 meters per second while the 15 Newtons pushing east will add a 7.5 meters per second eastward acceleration. The direction of the net acceleration will therefore be 5 units up for every 7.5 units right, which on an x,y plot would be a line with slope 5/(7.5)=2/3. The magnitude of the net acceleration can be found with pythagorus's help, as it is the hypotenuse of the right triangle with a vertical leg 5 units long (the units are meters/second^2) and a left pointing leg 7.5 units long.

(5^2+(7.5)^2)^(1/2) = (25+56.25)^(1/2) = (81.25)^(1/2) = 9.014

The acceleration of the object is therefore 9.014 meters per second squared and points east north east.

Hope this helps!

Joss

Answer 2

We need to calculate the addition of the two forces .

F1=10 N North

F2 = 15 N East

Draw a right angle triangle

Find the value of hypotenuse

F sum = sq rt (10²₊ 15² ) =sq rt 325 N

apply Newtons 2nd law to find the acceleration

a = Fsum / m