Question

The three forces (in units of N) given below are acting on a 20 kg mass. Calculate the magnitude of the acceleration of the mass. stack F subscript 1 with rightwards harpoon with barb upwards on top equals 3 i with hat on top space space space space space stack F subscript 2 with rightwards harpoon with barb upwards on top equals 5 j with hat on top space space space space stack F subscript 3 with rightwards harpoon with barb upwards on top equals open parentheses i with hat on top minus 3 j with hat on top close parentheses space space

Answer 1

Answer:

Acceleration, $a=0.223\ m/s^2$

Explanation:

Mass of the object, m = 20 kg

The forces acting on the objects are as follows :

$F_1=3i$

$F_2=5j$

$F_3=i-3j$

The net force acting on the object is, $F=4i+2j$

Let a is the acceleration of the mass. It can be calculated using the second law of motion as :

$F=ma$

$a=\dfrac{F}{m}$

$a=\dfrac{4i+2j}{20}$

$a=\dfrac{1}{5}i+\dfrac{1}{10}j$

$|a|=\sqrt{(\dfrac{1}{5})^2+(\dfrac{1}{10})^2}$

$a=0.223\ m/s^2$

So, the magnitude of the acceleration of the mass is $0.223\ m/s^2$. Hence, this is the required solution.