### 4.11 Equilibrium Applications of Newton's Laws of Motion**Problem Statement:**A spherical rock of mass 4.0 kg is suspended from a cord. A steady horizontal breeze pushes the rock so that the cord makes a constant angle of 3.7° with the vertical. Find the tension in the cord.**Hint:**The hint section corresponds to an input field where students can request additional help or guidance on how to approach the problem.**Solution:**The provided space hints that an answer field where students are expected to enter their calculated tension (in Newtons) in the cord can be found right by the problem statement.This problem involves applying Newton's Laws of Motion to achieve equilibrium. The following steps can be used to solve the problem:1. **Identify Forces**: Determine the forces acting on the rock—gravitational force (weight) and the tension in the cord. The tension in the cord has both vertical and horizontal components.2. **Vertical Component (T_y)**: The vertical component of the tension must balance the gravitational force: \( T_y = T \cos(3.7°) \) Where: - \( T \) is the tension in the cord. - \( T_y \) is the vertical component of the tension. - \( 3.7° \) is the angle the cord makes with the vertical.3. **Gravitational Force**: The gravitational force acting on the rock (weight) is: \( W = mg \) Where: - \( m = 4.0 \) kg (mass of the rock) - \( g = 9.8 \) m/s² (acceleration due to gravity) \( W = 4.0 \times 9.8 \) \( W = 39.2 \) N4. **Equating Forces**: Equate the vertical component of the tension to the gravitational force: \( T \cos(3.7°) = 39.2 \) N5. **Solve for Tension (T)**: \( T = \frac{39.2}{\cos(3.7°)} \) Use a calculator to find \( \cos(3.7°) \), and then solve for \( T \).After following these steps, you will find

Answered: Image /qna-images/answer/b99dc819-91ba-439c-b84f-75fb3b570a5a.jpg

A spherical rock of mass 4.0 kg is suspended from a cord. A steady horizontal breeze pushes the rock so that the cord makes a constant angle of 3.7° with the vertical. Find the tension in the cord. i N Hint

A spherical rock of mass 4.0 kg is suspended from a cord. A steady horizontal breeze pushes the rock so that the cord makes a constant angle of 3.7° with the vertical. Find the tension in the cord. i N Hint

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 box with a mass of 0.5 slugs lies on an inclined plane making an angle of 30o with the horizontal.…

A: We know that 1 slug =14.59 kg 0.5 slug= 7.29 kg

Q: The forces are in static equilibrium. The 140 lb force is directed along the x-axis and the 300 lb…

Q: A ball hangs from a 1.25 m string. If it is given a push at the bottom, what is the minimum speed…

Q: Due to a jaw injury, a patient must wear a strap that produces a net upward force of 5.00 N on his…

Q: The upper leg muscle (quadriceps) exerts a force of 1250 N, which is carried by a tendon over the…

Q: Consider the 52.0-kg mountain climber shown below. (a) Find the tension in the rope and the force…

Q: A 3000-lb car is sitting on a ramp with a 6-degree incline. Rounded to the nearest Ib, find the…

A: Given data: The weight of car (W) = 3000 lb Inclined angle (θ) = 6° Required: The magnitude of…

Q: shown, the mass of block 1 is m1 = 4.0 kg and the mass of block 2 is m2 = 8.0 kg. Block 1 sits on an…

Q: A box with a mass of 0.5 slugs lies on an inclined plane making an angle of 30o with the horizontal.…

A: Force = 10.985 N

Q: Consider the figure below. (a) Find the tension in each cable supporting the 504-N cat burglar.…

Q: The upper leg muscle (quadriceps) exerts a force of 1270 N, which is carried by a tendon over the…

Q: Bill gets a job delivering pizzas. The pizza companymakes him mount a sign on the roof of his car.…

A: The additional drag force is,

Q: A block is resting on a ramp as shown in the figure below. You can change the inclination angle by…

Q: A 33-kilogram concrete block A is kept from moving down the plane inclined at an angle e from the…

Q: (a) Calculate the tension (in N) in a vertical strand of spiderweb if a spider of mass 7.00 x 10-5…

A: Introduction: Tension is a force transmitted through a rope or a wire when pulled acts in the…

Q: Two packing crates of masses m, = 10.0 kg and m, = 7.10 kg are connected by a light string that…

Q: A 70 kg bicyclist is coasting down a long hill with a 1.9 ∘ slope. He's moving quite rapidly, so air…

A: Given: The mass of the bicyclist is m=70 kg. The angle of the slope is θ=1.9o. The cross-sectional…

Q: a large box of mass 11.4 kg sits on a ramp that makes an angle of 30.1 degrees with the horizontal.…

Q: A block is placed on a frictionless 30 degree incline.the mass of the block is m=30kg. b.find the…

Q: 8. A mass m₁ = 9.00 kg is connected by a light string that passes over a pulley of mass M = 14.0 kg…

A: Required value of tension acting on mass m2

Q: A snowboarder and his board with a combined mass of 50.0 kg moving at 9.50 m/s are about to go up an…

Q: Q.5. A uniform rod AB of weight W is hinged to a fixed point at A It is held in the horizontal…

A: Given: Weight of the rod AB =W One end of string is attached to B. Rod is hinged at fixed point A.

Q: A 16-year-old employee working for Southern Virginia College's (SVC) bookstore during the summer…

Q: Atraffic engineer wants to suspend a 200-lb traffic lightabove the center of the two right lanes of…

A: Given: W = 200 lb

Q: A sphere of mass 5.0 × 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the…

Q: A horizontal force of 5 kN is acting on the wedge, as shown in the figure. The coefficient of…

A: Given data: The force act on the wedge is 5 kN The coefficient of friction is μ=0.25

Question

### 4.11 Equilibrium Applications of Newton's Laws of Motion

**Problem Statement:**

A spherical rock of mass 4.0 kg is suspended from a cord. A steady horizontal breeze pushes the rock so that the cord makes a constant angle of 3.7° with the vertical. Find the tension in the cord.

**Hint:**

The hint section corresponds to an input field where students can request additional help or guidance on how to approach the problem.

**Solution:**

The provided space hints that an answer field where students are expected to enter their calculated tension (in Newtons) in the cord can be found right by the problem statement.

This problem involves applying Newton's Laws of Motion to achieve equilibrium. The following steps can be used to solve the problem:

1. **Identify Forces**: Determine the forces acting on the rock—gravitational force (weight) and the tension in the cord. The tension in the cord has both vertical and horizontal components.

2. **Vertical Component (T_y)**: The vertical component of the tension must balance the gravitational force:

\( T_y = T \cos(3.7°) \)

Where:
- \( T \) is the tension in the cord.
- \( T_y \) is the vertical component of the tension.
- \( 3.7° \) is the angle the cord makes with the vertical.

3. **Gravitational Force**: The gravitational force acting on the rock (weight) is:

\( W = mg \)

Where:
- \( m = 4.0 \) kg (mass of the rock)
- \( g = 9.8 \) m/s² (acceleration due to gravity)

\( W = 4.0 \times 9.8 \)
\( W = 39.2 \) N

4. **Equating Forces**: Equate the vertical component of the tension to the gravitational force:

\( T \cos(3.7°) = 39.2 \) N

5. **Solve for Tension (T)**:

\( T = \frac{39.2}{\cos(3.7°)} \)

Use a calculator to find \( \cos(3.7°) \), and then solve for \( T \).

After following these steps, you will find

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 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 painter stands on a scaffold hung by its ends from two vertical ropes A and P, 6 m apart. The scaffold weighs 200 N. The tension in A is 750 N and that in Pis 200 N. a) What is the weight of the painter? b) How far from A is he standing?
Calculate P required to move block A upward. Assume the coefficient of friction is 0.2 below block B. Neglect friction at all other contact surfaces. 30° P B 80 lb H₂ = 0.2 A 120 lb
An elevator is supported by a cable and moving downward through the elevator shaft at a constant speed. How does the upward tension force compare to the downward force of gravity? O The upward tension force is stronger than the downward force of gravity. The downward force of gravity is stronger than the upward tension force. The tension force and the force of gravity are of equal strength.
Two boxes (Box A = 9.7 kg and Box B = 5.4 kg) are connected by acord running over a pulley. The coefficient of kinetic friction betweenbox A and the table is 0.18. We ignore the mass of the cord and pulleyand any friction in the pulley, which means we can assume that a forceapplied to one end of the cord will have the same magnitude at theother end. We wish to find the tension of the cord while accelerating (inN), assuming the cord doesn’t stretch. As box B moves down, box Amoves to the right. Hint: Solve for the acceleration of the system first.
A 26.8 kg box sits on a ramp at an angle of 13° above the horizontal. If the coefficient of static friction between the box on the ramp is 0.215, what minimum applied force is required to keep the box at rest?
M 30° The pulley and all surfaces are frictionless. Suppose both blocks are made of solid gold. In addition, each block has a mass of 2.08 kg. Find the tension (in N) in the connecting the two gold blocks.
A model airplane of mass 0.3 kg is attachedto a horizontal string and flies in a horizontalcircle of radius 5.9 m, making 1.6 revolutionsevery 4 s. (The weight of the plane is balancedby the upward “lift” force of the air on thewings of the plane.)The accelaration due to the gravity is 9.81m/s2 Find the tension in the string.Answer in units of N.
(a) Calculate the tension (in N) in a vertical strand of spiderweb if a spider of mass 7.00 x 10-5 kg hangs motionless on it. (Enter a number.) (b) Calculate the tension (in N) in a horizontal strand of spiderweb if the same spider sits motionless in the middle of it much like the tightrope walker in the figure. 5.0° 5.0 TR y T Ta The strand sags at an angle of 12.0° below the horizontal. (Enter a number.) N Compare this with the tension in the vertical strand (find their ratio). (Enter a number.) (tension in horizontal strand)/(tension in vertical strand) =