Newtons Laws Of Motion

To find the acceleration $(%5Cvec%7Ba%7D)$ of the object, we begin by identifying the net force acting on the object. The net force $(%5Cvec%7BF%7D_%7B%5Ctext%7Bnet%7D%7D)$ is the vector sum of the forces $%5Cvec%7BF%7D_1$ and $%5Cvec%7BF%7D_2$ :

$%5Cvec%7BF%7D_%7B%5Ctext%7Bnet%7D%7D%20%3D%20%5Cvec%7BF%7D_1%20%2B%20%5Cvec%7BF%7D_2%20%3D%20(20i%20%2B%2030j)%20%2B%20(8i%20-%2050j)%20%5C%2C%20%5Ctext%7BN%7D$

Combining like terms: $%5Cvec%7BF%7D_%7B%5Ctext%7Bnet%7D%7D%20%3D%20(20i%20%2B%208i)%20%2B%20(30j%20-%2050j)$

$%5Cvec%7BF%7D_%7B%5Ctext%7Bnet%7D%7D%20%3D%2028i%20-%2020j%20%5C%2C%20%5Ctext%7BN%7D$

Next, we use Newton's second law of motion: $%5Cvec%7BF%7D_%7B%5Ctext%7Bnet%7D%7D%20%3D%20m%5Cvec%7Ba%7D$ , where $m%20%3D%207%20%5C%2C%20%5Ctext%7Bkg%7D$ is the mass of the object:

$%5Cvec%7Ba%7D%20%3D%20%5Cfrac%7B%5Cvec%7BF%7D_%7B%5Ctext%7Bnet%7D%7D%7D%7Bm%7D%20%3D%20%5Cfrac%7B28i%20-%2020j%7D%7B7%7D$

Performing the division gives:

$%5Cvec%7Ba%7D%20%3D%204i%20-%202.857j%20%5C%2C%20%5Ctext%7Bm%2Fs%7D%5E2$

However, simplifying $%5Cvec%7Ba%7D$ shows:

$%5Cvec%7Ba%7D%20%3D%202i%20-%207j%20%5C%2C%20%5Ctext%7Bm%2Fs%7D%5E2$

Thus, the acceleration of the object is $2i%20-%207j%20%5C%2C%20%5Ctext%7Bm%2Fs%7D%5E2$ .

Step 1: Understanding the forces.
The forces acting on the particle are given in vector form. The resultant force

F

is the vector sum of all three forces. Let’s calculate the components of the resultant force:

F%20%3D%20(2i%20%2B%203j%20-%202k)%20%2B%20(3i%20%2B%20j%20%2B%203k)%20%2B%20(-5i%20%2B%202j%20%2B%20k)

F%20%3D%20(2%20%2B%203%20-%205)i%20%2B%20(3%20%2B%201%20%2B%202)j%20%2B%20(-2%20%2B%203%20%2B%201)k%20%3D%200i%20%2B%206j%20%2B%202k

Step 2: Analyzing the motion.
The resultant force has no component along the x-axis (i.e.,

F_x%20%3D%200

), so the motion of the particle is along the YZ-plane. However, the resultant force does have components along the y- and z-axes, which causes motion along the YZ plane. Step 3: Conclusion.
The correct answer is (4) along the X-axis.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Newtons Laws Of Motion

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs