Question

The only two forces acting on a body have magnitudes of 20 N and 35 N and directions that differ by 80°. The resulting acceleration has a magnitude of 20 m/s2. What is the mass of the body? a. 2.4 kg b. 2.2 kg c. 2.7 kg d. 3.1 kg e. 1.5 kg

Answer 1

Answer:

The mass of the body is 2.2 kg.

Explanation:

Given that,

Force acting on a body 1, $F_1=20\ N$

Force acting on a body 2, $F_2=35\ N$

Direction, $\theta=80^{\circ}$

Acceleration, $a=20\ m/s^2$

To find,

Mass of the body.

Solution,

Let F is the net force acting on the body. It is given by :

$F=\sqrt{F_1^2+F_2^2+2F_1F_2\ cos\theta}$

$F=\sqrt{20^2+35^2+2\times 20\times 35\ cos(80)}$

F = 43.22 N

Second law of motion is given by :

F = ma

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

$m=\dfrac{43.22\ N}{20\ m/s^2}$

m = 2.16 kg

or

m = 2.2 kg

So, the mass of the body is 2.2 kg.