Question

Two ropes are attached to a 40-kg object. The first rope applies a force of 50 N and the second, 40 N. If the two ropes are perpendicular to each other, what is the resultant magnitude of the acceleration of the object?

Answer 1

To solve this problem we will use the concepts related to the resulting Vector Force product of two components, that is,

$|\vec{F}| = \sqrt{F_x^2+F_y^2}$

If we take the Force of 50 N as the force in the X direction and the Force of 40 N in the Y direction we will have to:

$|\vec{F}| = \sqrt{F_x^2+F_y^2}$

$|\vec{F}| = \sqrt{(50)^2+(40)^2}$

$|\vec{F}| = 64.03N$

Finally, since Newton's second law, acceleration can be determined as

$F = ma$

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

$a = \frac{ 64.03}{40}$

$a = 1.6m/s^2$

Therefore the resultant magnitude of the acceleration of the object is $1.6m/s^2$

Answer 2

The magnitude of the resultant acceleration of the object is 1.6 m/s².

What is acceleration?

Acceleration is the rate of change of velocity

To calculate the magnitude of the resultant acceleration of the object, first, we need to find the resultant force on the object.

Since the two forces acting on the object are perpendicular, the resultant  force is calculated as

• F' = √(40²+50²)
• F' = √(4100)
• F' = 64.03 N

Applying,

• a = F'/m................... Equation 1

Where:

• a = acceleration of the object
• m = mass of the object
• F' = Resultant force acting on the object.

From the question,

Given:

• m = 40 kg

Substitute into equation 1

• a = 64.03/40
• a = 1.6 m/s²

Hence, The magnitude of the resultant acceleration of the object is 1.6 m/s².

Learn more about acceleration here: https://brainly.com/question/19365526