Answer to Question #253986 in Mechanics | Relativity for unalome

Question

A 135-N block resting on a rough horizontal table is pulled by a horizontal wire. The

pull gradually increases until the block begins to move and continues to increase

thereafter. The figure below shows a graph of the friction force on this block as a

function of the pull.

a. Identify the regions of the graph where static and kinetic friction occur.

b. Find the coefficients of static and kinetic friction between the block and the table.

c. Why does the graph slant upward in the first part but then level out?

Answer 1

a.

From the given graph, the friction force is linearly increased from 0 N to 75 N with respect to pull force from 0 N to 75 N . When pull force is increasing the frictional force is also increasing from 0 N to 75 N . This means the frictional force is directly proportional to the pull force in this region. The region from point A to B , in which the body is in rest because the magnitude frictional force is equal to the applied force but direction is in opposite. The region in which, the frictional force acts on the rest body is known as the statics friction force.

When pull force is slightly increased than the 75 N, the frictional force is suddenly fall from 75 N to 50 N . After 75 N applied force, the frictional force is constant throughout the graph. This means that after a limit of applied force ( 75 N ) the frictional force is constant. The point at which the frictional force is maximum, that point is known as limiting point. When applied force is slightly increasing than the maximum friction force, the body will be start to moving. When body is moving, then the friction force acts on the object is less than the maximum friction force. The region in which, the friction force is acts on the moving body is known as the kinematics friction force.

Therefore, the region of graph from A to B is statics friction and the region of graph from C to D is kinematics friction.

b.

The following shows that free body diagram of the block is,

Formula to calculate the static friction force is,

$f_s = μ_s R$

f_s is the static frictional force.

R is normal reaction.

Equilibrium equation perpendicular to the horizontal surface is,

R − W = 0

R = W

R is the normal reaction.

W is the weight of the block.

Substitute m g for R to find f_s.

$f_s = μ_s W$

Substitute 75 N for f_s and 135 N for W to find μ_s.

$75 \; N = μ_s \times 135 \; N \\ μ_s = 0.55$

Thus, the coefficient of statics friction is 0.55.

Formula to calculate the kinetic friction force is,

$f_k = μ_k R$

f_k is the kinematics frictional force.

μ_k is the coefficient of kinematics friction.

Substitute 50 N for f k and 135 N for W to find μ_k.

$50 \; N = μ_k \times 135 \; N \\ μ_k = 0.37$

Thus, the coefficient of kinematic friction is 0.37 .

Therefore, the coefficient of statics friction and coefficient of kinematics friction is 0.55 and 0.37 respectively.

c.

From the given graph, the friction force is linearly increased from 0 N to 75 N with respect to pull force from 0 N to 75 N . When pull force is increasing the frictional force is also increasing from 0 N to 75 N . This means the frictional force is directly proportional to the pull force in this region. The region from point A to B , in which the body is in rest because the magnitude frictional force is equal to the applied force but direction is in opposite. The region in which, the frictional force acts on the rest body is known as the statics friction force.

When pull force is slightly increased than the 75 N , the frictional force is suddenly fall from 75 N to 50 N . After 75 N applied force, the frictional force is constant throughout the graph. This means that after a limit of applied force (75 N) the frictional force is constant. The point at which the frictional force is maximum, that point is known as limiting point. When applied force is slightly increasing than the maximum friction force, the body will be start to moving. When body is moving, then the friction force acts on the object is less than the maximum friction force. The region in which, the friction force is acts on the moving body is known as the kinematics friction force.

When block is in rest, the applied force is gradually increasing simultaneously the statics frictional force is also increasing. After a certain limit of applied force the frictional force reach at the maximum value. Again, slightly increasing the applied force the block will be tends to start moving.

When the block is start moving the frictional force is decreases suddenly because when object is in rest the chemical bond formation between the surface of block and earth. When we applied a certain limit of force the bond will be break down. After the bond is breaking down the body will be start moving then again the bond is not formed. Therefore, the graph first silent up but then level out due to more force is required to break the bond.