Question

Q1: When two objects slide against oneanother, which of the following statements about the force offriction between them is true?

Themagnitude of the frictional force is always equal to $\mu_{\rm k}n$ . Themagnitude of the frictional force is always less than $\mu_{\rm k}n$ . Themagnitude of the frictional force is determined by other forces onthe objects so it can be either equal to or less than $\mu_{\rm k}n$ .

Q2: When two objects are in contact with norelative motion, which of the following statements about thefrictional force between them is true?

Themagnitude of the frictional force is always equal to $\mu_{\rm s}n$ . Themagnitude of the frictional force is always less than $\mu_{\rm s}n$ . Themagnitude of the frictional force may be either equal to or lessthan $\mu_{\rm s}n$ .

Q3: When a board with a box on it is slowly tilted to a largerand larger angle, common experience shows that the box will at somepoint "break loose" and start to accelerate down the board. The boxbegins to slide once the component of its weight parallel to theboard, $w_$ , equals the maximum force of static friction. Which ofthe following is the most general explanation for why the boxaccelerates down the board after it begins to slide(rather than sliding with constant speed)?

Once the boxis moving, $w_$ is less than the force of static friction but greaterthan the force of kinetic friction. Thecoefficient of kinetic friction is less than the coefficient ofstatic friction. When the boxis stationary, $w_$ equals the force of static friction, but once the boxstarts moving, the sliding reduces the normal force, which in turnreduces the friction. Once the boxis moving, $w_$ is greater than the force of static friction but lessthan the force of kinetic friction.

Please help! I got 8 wrongs already!

Answer 1

Concepts and reason

The concept used here are Kinetic friction, Static friction, Newton’s second law and Newton’s third law.

Use the properties of different frictional forces acing on the bodies are in contact and moving and conclude the correct statements.

Fundamentals

The kinetic friction acts between the bodies contact moving with constant motion.

The static friction acts between the bodies contact which have no relative motion.

The force exerted by one body on another body is known as the normal force when they are in contact with each other.

The kinetic friction is the friction force between sliding surfaces which is given as follows:

Here, is the coefficient of kinetic friction, and is the normal force.

The static friction is the friction force between surfaces with no relative motion which is given as follows:

Here, is the coefficient of static friction, and is the normal force.

The force of gravitation of the earth on a body is,

Here, is the mass and is the acceleration due to gravity.

The equilibrium force condition perpendicular to the incline plane is,

Here, is sum of all the forces acting perpendicular to the plane.

(Q1)

The force acting between the two sliding objects which are in contact with each other is the normal force and hence, the frictional force acts between the two surfaces which opposes their motion.

Hence, the frictional force always equal to

(Q2)

The actual magnitude of the friction F is such that it, together with any other forces present, will cause the object to have zero acceleration. The magnitude of the force due to static friction cannot, however, exceed .

Hence, the frictional force between the two objects with no relative motion is less than or equal to the

(Q3)

The frictional force acting on the box which is sliding is less compared to the frictional force acting on the box at rest. Hence, the box starts accelerating down.

Thus, the coefficient of the kinetic friction is less than the coefficient of the static friction when the box starts accelerating down the board.

Ans: Part Q1

The frictional force is always equal to .

Part Q2

The frictional force between the two objects with no relative motion is less than or equal to the .

Part Q3

The coefficient of the kinetic friction is less than the coefficient of the static friction when the box starts accelerating down the board.