We appreciate your visit to A wedge of mass tex m 37 1 text kg tex is located on a plane that is inclined by an angle tex theta 20. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The acceleration of the wedge along the inclined plane, considering gravitational, normal, frictional, and applied forces, is approximately 4.76 m/s^2.
To determine the acceleration of the wedge along the inclined plane, Newton's second law is applied, stating that the net force on an object is the product of its mass and acceleration. Considering the forces acting on the wedge:
Gravitational force pulling the wedge downward along the inclined plane.
Normal force perpendicular to the plane.
Frictional force opposing motion along the plane.
Horizontal force applied externally.
First, resolve forces perpendicular and parallel to the inclined plane:
Perpendicular to the plane: N = mg * cos(theta), where N is the normal force, m is the mass of the wedge, g is the acceleration due to gravity, and theta is the angle of inclination.
Parallel to the plane: F_parallel = mg * sin(theta), force parallel to the plane.
Calculate frictional force using the coefficient of friction (mu):
Frictional force: f_friction = mu * N
Now, determine the net force along the plane:
Net force: F_net = F - f_friction = ma
Substitute expressions for F_parallel and f_friction into the net force equation:
a = (F - mu * mg * cos(theta)) / m
Now, plug in the given values:
a = (311.3 - 0.153 * 37.1 * 9.81 * cos(20.5)) / 37.1
a ≈ (311.3 - 0.153 * 37.1 * 9.81 * 0.9397) / 37.1
a ≈ (311.3 - 134.49) / 37.1
a ≈ 176.81 / 37.1
a ≈ 4.76 m/s^2
Therefore, the acceleration of the wedge along the plane is approximately 4.76 m/s^2.
Thanks for taking the time to read A wedge of mass tex m 37 1 text kg tex is located on a plane that is inclined by an angle tex theta 20. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
