Question

1.) A box with a mass of 5 kg only has three forces acting on it:

- One force of 16 N due East.
- One force of 24 N due South.
- One force of 39 N due East

What is the magnitude of the box's acceleration, in
m/s^{2}?

Write the number and not the units.

2.) A box with a mass of 10 kg only has two forces acting on it:

- One force of 15 N due East.
- One force of 45 N due West.

What is the magnitude of the box's acceleration, in
m/s^{2}?

Write the number and not the units.

Answer #1

**Answer:-**

**1) 12**

**2) 3**

**Solution:-**

**1)**

let east direction is positive x-axis, then west will be negative x-axis.North and South will be positive and negative y-axis respectively.

now, Fx = 16 + 39 = 55 N

Fy = - 24 N

F = √(Fx² + Fy²)

F = √(55² + (-24)²)

F = 60 N

using Newton's second law,

F = m*a

60 = 5 * a

solving for a,

a = 12 m/s²

As you only need magnitude and not units so the answer is 12.

**2)**

in this case,

Fx = 15 - 45 = -30 N

Fy = 0 N

F = 30 N

using Newton's second law,

F = m*a

30 = 10 * a

a = 3 m/s²

the acceleration of the box is 3.

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