Forces in Circular Motion and Friction

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Questions and Answers

What is the correct formula for a variation in force $dF$ when the radius $r$ is held constant and the period $T$ changes?

dF = $-mv^{2} rac{dT}{3 ext{π}r^{2}}$

dF = $2mv r dT$

dF = $-mv^{3}rac{dT}{ ext{π}r^{2}}$ (correct)

dF = $-mv^{3} rac{dT}{2 ext{π}r^{2}}$

If the tension in the upper string connected to a rotating rod is 37 N, what is the tension in the lower string if the ball is 1.35 kg?

25.0 N

37 N

10.5 N (correct)

11.0 N

Given that the speed of the ball is 6.70 m/s, what would most affect the net force acting on the ball?

The length of the strings

The distance between the two strings

The angle of the strings

The mass of the ball (correct)

What is the relationship between the net force acting on the ball and its speed during uniform circular motion?

Net force increases as speed increases Signup and view all the answers

At the top of a circular hill, if the normal force on the driver is 0, what can be deduced about the forces acting on the driver?

Centripetal force is provided entirely by gravitational force Signup and view all the answers

If the normal force at the bottom of the valley needs to be calculated, which factor is most crucial?

All of the above Signup and view all the answers

Which of these scenarios exemplifies an increase in centripetal force?

Decreasing the radius while increasing speed Signup and view all the answers

What does a net force of 41.1 N indicate about the forces acting on the ball?

There is an unbalanced force causing acceleration Signup and view all the answers

What is the relationship between speed and the period of an object in uniform circular motion?

Speed is inversely proportional to the period. Signup and view all the answers

What must the coefficient of static friction be for a car weighing 1000 kg to safely round a curve with a radius of 50 m at a speed of 14 m/s?

0.4 Signup and view all the answers

If the pavement is icy and the coefficient of static friction is 0.25, what is the maximum speed a 1000 kg car can achieve while rounding the curve?

10 m/s Signup and view all the answers

What physical force must act on a car moving in a circular path to maintain its motion around the curve?

Frictional force Signup and view all the answers

At the top of the arc, how does the tension in the cord of a ball compare to the gravitational force acting on it?

Tension is less than gravitational force. Signup and view all the answers

Which component affects the tension in the cord of an object moving in uniform circular motion at the bottom of the arc?

Both the mass and speed of the object. Signup and view all the answers

For a constant radius in circular motion, which statement about speed and angular velocity is true?

Speed decreases as angular velocity decreases. Signup and view all the answers

What is the resulting effect of increased radius on the speed of an object in circular motion?

Increased radius allows for higher maximum speed. Signup and view all the answers

What is the tension in the cord when the mass of the block is 9.5 kg and the angle is 30°?

46.6 N Signup and view all the answers

What is the normal force acting on the block when its mass is 9.5 kg?

80.7 N Signup and view all the answers

If the cord is cut, what is the magnitude of the resulting acceleration of the block?

4.9 m/s² Signup and view all the answers

Which of the following statements is true regarding the best submission for each question part?

Your best submission for each part is used for your score. Signup and view all the answers

What happens to the number of submissions remaining for each question part?

It changes when a submission or change is made. Signup and view all the answers

What important action should you take before viewing the answer key?

Request an extension if needed. Signup and view all the answers

What does not automatically grant an extension for an assignment?

Viewing the answer key Signup and view all the answers

In the context of the assignment, what should you consider before viewing your work after the due date?

Extension policies Signup and view all the answers

What is the minimum force required to start moving a 63 kg crate if the coefficient of static friction is 0.49 and the rope is inclined at 13° above the horizontal?

279 N Signup and view all the answers

If a pig slides down a 29° slide in twice the time it would take on a frictionless slide, what is the coefficient of kinetic friction between the pig and the slide?

0.42 Signup and view all the answers

What happens if a student has viewed the answer key regarding extension requests?

No extension will be granted. Signup and view all the answers

When a train moving at 49 km/h comes to a stop, what is the maximum distance it can stop at constant acceleration without causing crates to slide, assuming a static friction coefficient of 0.21?

45.0 m Signup and view all the answers

If the coefficient of kinetic friction for the crate is 0.34, what is the magnitude of the initial acceleration of the crate?

1.32 m/s² Signup and view all the answers

What is the significance of the angle at which the rope is pulled when attempting to move the crate?

It impacts the weight component parallel to the surface. Signup and view all the answers

In teaching dynamics, what could be a possible consequence of not understanding the application of friction correctly?

Improper calculations leading to erroneous results. Signup and view all the answers

Why is it important to understand both static and kinetic friction while studying motion?

Understanding both helps in predicting the behavior of objects. Signup and view all the answers

What is the effect of varying the coefficient of static friction (𝜇s) on the maximum velocity (vmax) for bank angles between 0° to 50°?

Higher 𝜇s increases vmax for all angles. Signup and view all the answers

What constant velocity condition is necessary for the mop head to move without frictional forces causing acceleration?

The applied force must equal the kinetic friction force. Signup and view all the answers

Which bank angle and coefficient of friction yield the maximum speed of 141 km/h?

𝜃 = 4°, 𝜇s = 0.58 Signup and view all the answers

What happens to the maximum speed (vmax) as the bank angle (𝜃) increases when the coefficient of friction remains constant?

Vmax increases to a point and then decreases. Signup and view all the answers

Which equation accurately represents the force applied to the mop given the angle 𝜃?

F = 𝜇k m g \sin(𝜃) - 𝜇k m g \cos(𝜃) Signup and view all the answers

What condition must be met for the mop to be unable to move when a force is applied along its handle?

The angle 𝜃 must be less than a critical angle 𝜃0. Signup and view all the answers

At which bank angle did the evaluation of maximum speed for wet or icy conditions yield 108 km/h?

𝜃 = 0° Signup and view all the answers

Which implication is suggested regarding driver behavior on wet or icy roads based on vmax evaluations?

Drivers will often not realize the risks of reduced vmax. Signup and view all the answers

Study Notes

### Forces in Circular Motion

The force required to keep an object moving in a circle is called the centripetal force
The force is directed towards the center of the circle
The centripetal force is equal to the mass of the object times the square of its velocity divided by the radius of the circle
The equation for centripetal force is: F = mv^2/r

### Friction

Static friction occurs when an object is at rest and the applied force is less than the maximum static friction force
Kinetic friction occurs when an object is moving and the applied force is greater than the maximum static friction force
The coefficient of static friction is the ratio of the maximum static friction force to the normal force
The coefficient of kinetic friction is the ratio of the kinetic friction force to the normal force

Introduction to Forces

The force of gravity is the force that attracts objects together
The acceleration due to gravity is 9.8 m/s^2
The force of gravity is equal to the mass of the object times the acceleration due to gravity
The equation for the force of gravity is: F = mg

Inclines

The angle of an incline is the angle between its surface and the horizontal
The force of gravity acting on an object on an incline can be resolved into components parallel and perpendicular to the incline
The component of gravity parallel to the incline is equal to the mass of the object times the acceleration due to gravity times the sine of the angle of the incline
The component of gravity perpendicular to the incline is equal to the mass of the object times the acceleration due to gravity times the cosine of the angle of the incline

### Uniform Circular Motion

An object in uniform circular motion moves at a constant speed in a circular path
The acceleration of an object in uniform circular motion is always directed towards the center of the circle
The magnitude of the acceleration of an object in uniform circular motion is equal to the square of its velocity divided by the radius of the circle
The equation for the acceleration of an object in uniform circular motion is: a = v^2/r

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Description

This quiz covers the principles of forces in circular motion, including centripetal force and its equation. Additionally, it addresses static and kinetic friction, highlighting their characteristics and coefficients. Test your understanding of these essential physics concepts.