Question

A Friction Experiment During an experiment, a crate is pulled along a rough horizontal surface by a force F⃗ and the magnitude of the acceleration along the x direction, ax , is measured.(Figure 1) The vector F⃗ has a component along the x direction of magnitude Fx . The experiment is repeated several times, with different values of Fx each time, while maintaining a constant value for, Fy , the vertical component of F⃗ .

Part A Create a plot of the force of static friction, fs , versus the x component of the pulling force, Fx , for the experiment. Let the point Fmin , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship among fs , Fx , and Fmin . (Figure 2) Please ChooseA B C D E SubmitHintsMy AnswersGive UpReview Part Part B Create a plot of the force of kinetic friction, fk , versus the x component of the pulling force, Fx , for the experiment. Let the point Fmin , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship among fk , Fx , and Fmin . (Figure 3) Please ChooseA B C D SubmitHintsMy AnswersGive UpReview Part Part C After all the trials are completed, a graph of acceleration ax as a function of force Fx is plotted. Assuming the presence of both static and kinetic friction, which of the following graphs (Figure 4) is most nearly correct? Please ChooseA B C D SubmitHintsMy AnswersGive UpReview Part Provide FeedbackContinue

Figure 1Figure 2Figure 3Figure 4 of 4 A Friction Experiment During an experiment, a crate is pulled along a rough horizontal surface by a force F⃗ and the magnitude of the acceleration along the x direction, ax , is measured.(Figure 1) The vector F⃗ has a component along the x direction of magnitude Fx . The experiment is repeated several times, with different values of Fx each time, while maintaining a constant value for, Fy , the vertical component of F⃗ . Part A Create a plot of the force of static friction, fs , versus the x component of the pulling force, Fx , for the experiment. Let the point Fmin , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship among fs , Fx , and Fmin . (Figure 2) Please ChooseA B C D E SubmitHintsMy AnswersGive UpReview Part Part B Create a plot of the force of kinetic friction, fk , versus the x component of the pulling force, Fx , for the experiment. Let the point Fmin , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship among fk , Fx , and Fmin . (Figure 3) Please ChooseA B C D SubmitHintsMy AnswersGive UpReview Part Part C After all the trials are completed, a graph of acceleration ax as a function of force Fx is plotted. Assuming the presence of both static and kinetic friction, which of the following graphs (Figure 4) is most nearly correct? Please ChooseA B C D SubmitHintsMy AnswersGive UpReview Part Provide FeedbackContinue Figure 1Figure 2Figure 3Figure 4 of 4

Answer 1

Concepts and reason

The concept required to solve this question is frictional forces and Newton’s second law of motion.

The static friction is the frictional force that comes from interlocking of the irregularities of the two surfaces in contact and prevents any relative motion some limit occurs, where the motion starts. For the lower applied forces the static friction matches the applied force until the threshold of the motion.

Kinetic friction occurs the two rough surfaces are moving with respect to each other. Once the motion starts, frictional resistance decreases and it is approximately constant for some range of speeds.

Fundamentals

The relationship between minimum force ${F_{\min }}$ required to start the motion is related to normal reaction N by following relation:

${F_{\min }} = {\mu _s}N$

Here, ${\mu _s}$ is the coefficient of static friction.

The kinetic friction ${f_k}$ is given as the product of coefficient of kinetic friction ${\mu _k}$ and normal reaction N.

${f_k} = {\mu _k}N$

The relation between applied force ${F_x}$ and acceleration ${a_x}$ by balancing the forces according to the Newton’s second law of motion is given as follow:

${F_x} - {f_k} = m{a_x}$

(A)

The plot between static friction and pulling force in x- direction is given below:

From this plot, both static friction and applied force along the interface is proportional to each other and a point comes when static friction becomes zero.

(B)

The plot between kinetic friction and pulling force in x- direction is given below:

In this plot, the kinetic friction is zero for the force less than ${F_{\min }}$ and attains a constant value after the motion starts.

(C)

The plot between acceleration ${a_x}$ and pulling force in x- direction is given below:

In this plot, the acceleration is zero for the force less than ${F_{\min }}$ and increases with increase in force after that.

Ans: Part A

The graph D is correct, as in it the frictional force is balanced by static friction up to ${F_{\min }}$ .