Question

The only force acting on a 10kg object has components Fx = 15N and Fy = 25N. Find the acceleration of the object.

Answer 1

Given :

▪ Mass of object = 10kg

▪ Force along x-axis = 15N

▪ Force along y-axis = 25N

To Find :

➳ Acceleration of the object.

SoluTion :

⇒ First we have to find out resultant force acts on the body.

⇒ Angle b/w force components = 90°

✴ Resultant force :

$\leadsto\sf\:F=\sqrt{(F_x)^2+(F_y)^2+2(F_x)(F_y)\cos90\degree}$

$\leadsto\sf\:F=\sqrt{15^2+25^2+2(15)(25)(0)}$

$\leadsto\sf\:F=\sqrt{225+625+0}$

$\leadsto\sf\:F=\sqrt{850}$

$\leadsto\bf\:F=29.15\:N$

✴ Acceleration of object :

➢ As per newton's second law of motion, Force is defined as the product of mass and acceleration.

$\dashrightarrow\sf\:F=ma$

$\dashrightarrow\sf\:29.15=10\times a$

$\dashrightarrow\boxed{\bf{a\approx 3\:ms^{-2}}}$

Answer 2

Given :-

• Mass of object (m) = 10kg
• Force along x - axis (Fx) = 15N
• Force along y - axis (Fy) = 25N

To Find :-

• Calculate the acceleration of the object = ?

Solution :-

We know that,

Angle between from components is 90° .

.°. Cos = 90° .

Now, We need to find Resultant Force acts on body.

$\ \tt \: F \: = \sqrt{(Fx) {}^{2} + (Fy) {}^{2} + 2(Fx)(Fy)cos90 \degree }$

$\tt \: F \: = \sqrt{(15) {}^{2} + (25) {}^{2} + 2(15)(25)(0) }$

$\tt \: F \: = \sqrt{225 + 625 + 0}$

$\tt \: F \: = \sqrt{850}$

$\tt \: \red{{F \: = 29.15N}}$

Applying Newton's second law of motion,

$\tt \: F \: = \: ma$

$\tt \: 29.15 \: = 10 \: \times a$

$\tt \: a \: = \frac{29.15}{10}$

$\tt \: \green{ a \: = 3 \: m/s {}^{2} (Approx)}$

Therefore, The acceleration of the object is 3m/s².