Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A box is pulled up a rough ramp that makes an angle of 22 degrees with the horizontal surface. The surface of the ramp is the [tex]$x$[/tex]-plane.

What is the magnitude of the force of tension if the net force in the [tex]$x$[/tex] direction is [tex]$98 N$[/tex]?

A. [tex]$57 N$[/tex]
B. [tex]$139 N$[/tex]
C. [tex]$178 N$[/tex]
D. [tex]$183 N$[/tex]


Sagot :

To solve this problem, we need to find the magnitude of the force of tension, given that the net force in the [tex]\( x \)[/tex]-direction is [tex]\( 98 \, \text{N} \)[/tex] and the ramp makes an angle of [tex]\( 22^\circ \)[/tex] with the horizontal.

1. Understanding the given data:
- The angle of the ramp, [tex]\(\theta\)[/tex], is [tex]\( 22^\circ \)[/tex].
- The net force in the [tex]\( x \)[/tex]-direction, [tex]\( F_{\text{net},x} \)[/tex], is [tex]\( 98 \, \text{N} \)[/tex].

2. Relate the net force to the tension force:
- The net force in the [tex]\( x \)[/tex]-direction is the component of the tension force (T) along the ramp direction.
- This relationship can be expressed as: [tex]\( F_{\text{net},x} = T \cos(\theta) \)[/tex].

3. Rearrange the formula to solve for the tension force (T):
- [tex]\( T = \frac{F_{\text{net},x}}{\cos(\theta)} \)[/tex].

4. Convert the angle from degrees to radians for accurate computation in trigonometric functions:
- [tex]\( \theta = 22^\circ \)[/tex] is equivalent to [tex]\( 0.383972435 \)[/tex] radians.

5. Calculate the tension force:
- Using the provided data, [tex]\( T \approx 105.69640478240318 \)[/tex].

Hence, the magnitude of the force of tension is approximately [tex]\( 105.696 \, \text{N} \)[/tex], which does not exactly match any of the given multiple-choice options but is closest to [tex]\( 57 \, \text{N} \)[/tex]. Given that this could be a trick or conceptual error in the problem options themselves, ensure to verify if any additional detail or conversion was intended in the problem.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.