### Finding the Magnitude and Direction of the Resultant Force**Problem Statement:**The particle shown below is at rest, where \( F_1 = 6.95 \, \text{N} \) and \( F_2 = 10.4 \, \text{N} \). Find the magnitude and direction of the resultant force \( F \).**Given:**- \( F_1 = 6.95 \, \text{N} \)- \( F_2 = 10.4 \, \text{N} \)**Diagram Description:**In the provided diagram:- There is a coordinate system with the \( y \)-axis oriented vertically and the \( x \)-axis oriented horizontally.- A particle is positioned at the origin.- There are two forces acting on the particle, \( F_1 \) and \( F_2 \): 1. \( F_1 \): This force is applied at an angle of \( 30.0^\circ \) counterclockwise from the negative \( x \)-axis. 2. \( F_2 \): This force is applied at an angle of \( 45.0^\circ \) clockwise from the positive \( x \)-axis.**Graphical Representation:**The diagram features arrows representing the forces:- \( F_1 \) is directed towards the left, slanting upward from the horizontal line.- \( F_2 \) is directed towards the left, slanting downward from the horizontal line.- The resultant force \( F \) is indicated, but its magnitude and direction are unknown.**Calculations:**To find the magnitude and direction of \( F \), you would typically resolve \( F_1 \) and \( F_2 \) into their vector components, sum these components, and then determine the magnitude and direction of the resulting vector.**Magnitude Calculation:**\[ F = \sqrt{(F_{1x} + F_{2x})^2 + (F_{1y} + F_{2y})^2} \]**Direction Calculation:**\[ \theta = \text{atan2}(F_{1y} + F_{2y}, F_{1x} + F_{2x}) \]Where \( F_{1x}, F_{1y}, F_{2x}, \) and \( F_{2y

Answered: Image /qna-images/answer/d24ba8d0-2f80-454d-9a92-d712d3a995e9.jpg

Answered: The particle shown below is at rest,…

The particle shown below is at rest, where F₁ = 6.95 N, and F₂ = 10.4 N. Find the magnitude and direction of F. magnitude direction F₁ 30.0° 45.0° counterclockwise from the +x-axis F x

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A small ball rolls horizontally off the edge of a tabletop that is 1.20 m high at t = Os. It strikes…

A: Since you have posted a question with a multiple sub parts, we will solve first three sub - parts…

Q: Determine the velocity total acceleration

A: Given: Radius of circular path is r=2.75 m Angular coordinate is α=24° Magnitude of acceleration is…

Q: You are at the top of the Empire State Building on the 102nd floor, which is located 373 m above the…

A: When the super hero is moving with the speed v, the height of the super hero as measured by us is…

Q: A light ray travels across the interface between two transparent materials as shown below. Note that…

A: When the light ray is not refracted, the incidence angle and the refracted angle will be the same.

Q: A pinball bounced around its machine before resting between two bumpers. Before the ball came to…

Q: A particle is launched from the origin on the ground with an initial velocity v = (2.40 m/s) x +…

A: For a freely falling projectile particle launched at an angle θ from the ground with an initial…

Q: You walk in the direction of the unit vector (1, 0, 0) a distance of 24 m at a constant speed of 3.0…

Q: An artillery shell is fired with an initial velocity of 300 m/s at 54.5° above the horizontal. To…

A: Shell moves in the horizontal direction with the constant velocity component, so acceleration in x…

Q: A car initially traveling eastward turns north by traveling in a circular path at uniform speed as…

Q: A projectile fred from the point (0.0) at an angle to the positive x-axis has a trajectory given by…

Q: In one contest at the county fair, a spring-loaded plunger launches a ball at a speed of 3.1 m/s…

A: Given data: Launching speed of ball, vo=3.1 m/s Elevation of board, ϕ=20o Range, R=2.2 m

Q: An artillery shell is fired with an initial velocity of 300 m/s at 50.0° above the horizontal. To…

Q: Let V⃗ 1 = -6.5 i + 8.3 j and V⃗ 2 = -4.9 j + 4.4 i. a)Determine the direction of V⃗ 1.…

Q: Don't use chatgpt will upvote and provide solution in Handwritten form neat and clean and please be…

A: Step 1:

Q: A person is rowing across the river with a velocity of 4.5 km/hr northward. The river is flowing…

A: directions of the person's rowing (North) and the direction of the river's flow (East) are…

Q: COMPLETE THE TABLE : GIVEN F1=142,100 AT 20 DEG F2=102,900 AT 105 DEG F3= 53, 900 AT 197 DEG…

A: Since you have not mentioned anything about the Equilibrant (Force table) and Resultant (Force…

Q: Ad - 250 m wide river flows with a uniform speed of 1₁ - 4.0 m/s toward the east. I take off from…

Q: There is a tree in the middle of your front yard and you take pictures of a squirrel as it runs…

A: d1 = 12 m @30o N of E d2 = 7.5 m @15o E of Stime (t) = 20 seconds

Q: An artillery shell is fired with an initial velocity of 300 m/s at 56.5° above the horizontal. To…

A: Given data The initial velocity of the artillery shell is: u = 300 m/s The angle of projection of…

Q: Passengers on the deck of a boat with a speed of Vs= 20⁡ m/s with the given direction experience a…

Q: ystem be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout…

Q: 1) An arm OA rotates around the origin O according to the angle 2 0.15t where 0 is in radians and t…

A: Given,In polar coordinates, the velocity vector of the collar at time t,

Q: The particle shown below is at rest, where F1 = 6.90 N, and F2 = 10.7 N. Find the magnitude and…

Question

### Finding the Magnitude and Direction of the Resultant Force

**Problem Statement:**
The particle shown below is at rest, where \( F_1 = 6.95 \, \text{N} \) and \( F_2 = 10.4 \, \text{N} \). Find the magnitude and direction of the resultant force \( F \).

**Given:**

- \( F_1 = 6.95 \, \text{N} \)
- \( F_2 = 10.4 \, \text{N} \)

**Diagram Description:**

In the provided diagram:

- There is a coordinate system with the \( y \)-axis oriented vertically and the \( x \)-axis oriented horizontally.
- A particle is positioned at the origin.
- There are two forces acting on the particle, \( F_1 \) and \( F_2 \):

1. \( F_1 \): This force is applied at an angle of \( 30.0^\circ \) counterclockwise from the negative \( x \)-axis.
2. \( F_2 \): This force is applied at an angle of \( 45.0^\circ \) clockwise from the positive \( x \)-axis.

**Graphical Representation:**
The diagram features arrows representing the forces:

- \( F_1 \) is directed towards the left, slanting upward from the horizontal line.
- \( F_2 \) is directed towards the left, slanting downward from the horizontal line.
- The resultant force \( F \) is indicated, but its magnitude and direction are unknown.

**Calculations:**
To find the magnitude and direction of \( F \), you would typically resolve \( F_1 \) and \( F_2 \) into their vector components, sum these components, and then determine the magnitude and direction of the resulting vector.

**Magnitude Calculation:**
\[ F = \sqrt{(F_{1x} + F_{2x})^2 + (F_{1y} + F_{2y})^2} \]

**Direction Calculation:**
\[ \theta = \text{atan2}(F_{1y} + F_{2y}, F_{1x} + F_{2x}) \]

Where \( F_{1x}, F_{1y}, F_{2x}, \) and \( F_{2y

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: given

VIEW

Step 2: calculation

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A projectile is fired horizontally to the west at a velocity of 35 m/s. What is the horizontal velocity of the projectile after 6 seconds? Direction: What is the magnitude of the vertical velocity of the projectile after 6 seconds? Direction:
An arrow is shot into the air at an angle of 59.8° above the horizontal with a speed of 21.5 m/s. What is the x-component of the velocity of the arrow 3.30 s after it leaves the bowstring? What is the y-component of the velocity of the arrow 3.30 s after it leaves the bowstring? What is the x and y-component of the displacement of the arrow during the 3.30-s interval? What is the y-component of the displacement of the arrow during the 3.30-s interval?
The following picture shows the acceleration, a, and velocity, v, vector at several points along an object's curved trajectory. The dotted lines at each point are perpendicular to the trajectory. 2 7 a 1 At which point is the acceleration vector impossible? O Point 3 O Point 1 O Point 5 O Point 2 ⒸPoint 4 a = 0 Z 4 100 100 5
An apple grows on a tree located on a 42° hill with respect to the horizontal. The apple falls, hitting the ground with a downward velocity at 6.87 m/s. The apple's impact velocity can be resolved into components parallel and perpendicular to the hill. Find the magnitude of the parallel component, v
The position functions of four particles are given as follow. Which of the particles have constant acceleration? Particle 1: (t) = 3.1 – 2.7 %3D Particle 2: (t) = 3.5 + 1.4t Particle 3: (t) = 3.1 – 2.7t2 Particle 4: z(t) = 3.5 – 3.4t - 1.4t All of them O only 3 and 4 O only 2 and 3 only 1 and 2
1. The coordinates of a particle moving in the XY plane are given as function of time by: X = 5m + ( 7 m/s^4) t ^4 Y = ( 10 m/s)t + (3 m/s^5)t ^5 Find the position vector of the body at t = 3.5 sec. ( first answer is X, followed by Y) Your answer
The particle shown below is at rest, where F₁ magnitude direction F₁ 30.0° 45.0° F2 X 6.35 N, and F2 = 11.5 N. Find the magnitude and direction of F. o counterclockwise from the +x-axis F
A fighter plane moving 211.0 m/s horizontally fires a projectile with speed 47 m/s in a forward direction 30.0° below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground? a) 240 m/s b) 283 m/s c) 253 m/s d) 278 m/s
Part A - A mortar positioned on the valley floor fires a shell that hits the top edge of a steep canyon. Initially the shell has a speed of 269 m/s and is shot at an angle of 65° above the horizontal. A soldier using a map determines the horizontal distance from the mortar to the canyon's edge is 2900 m. How high above the valley floor did the shell hit? ΑΣφ ? m Submit Request Answer
Birdman is flying horizontally at a speed of 33 m/s and a height of 63 m. Birdman releases a egg directly over the start of the field. How far from the start of the field should the robot hold the bucket to catch the egg
Question 013A: Complete the following question involving vectors and net force. A boat travels towards the northeast at 23 knots, and there is an 8 knot crosswind out of the southeast affecting the boat. Convert the boat's motion (not the crosswind) into rectangular coordinates (aka: convert into "X" and "y"). O x = -16.26 y = -16.26 O x = 16.26 y = 16.26 O x = 0 y = 23 x = 16.26 y = -16.26 QUESTION 14 Question 013B: Complete the following question involving vectors and net force. A boat travels towards the northeast at 23 knots, and there is an 8 knot crosswind out of the southeast affecting the boat. Convert the crosswind (not the boat) into rectangular coordinates (aka: convert into "x" and "y"). O x = 5.66 y = -5.66 O x = -4 y = 4 O x = -5.66 у--5.66 O x = -5.66 y = 5.66
A ship sets sail from Rotterdam, The Netherlands, heading due north at 8.5 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0° north of east. What is the magnitude of the velocity of the ship relative to the Earth in m/s? What is the angle of the velocity of the ship relative to the Earth in degrees N of E?