3.3.2 Problems on Friction and Inclines

Question 1

Problems on Friction and Inclines

Answer 1

• A block on an incline with friction remains motionless until the incline reaches a critical angle. Beyond this angle, the block accelerates down the ramp.
• The magnitude of static friction depends on the magnitude of other forces. As the angle of the incline q increases, so does fs. The static frictional force of an object on an incline is given by the formula .
• The acceleration of a block down an incline is

Question 2

Which of the following statements regarding kinetic friction is not correct?

Answer 2

The coefficient of kinetic friction is a dimensionless constant of proportionality between the frictional force acting on a moving object and its weight

Question 3

The force diagram shows a block of wood on an incline. Formulas for Wx and Wy are shown.

Using Newton’s second law we can derive the following equations:
Fx = max

-fs + mg sin θ = 0
fs = + mg sin θ
fs = +mg sin θc
fs1max = msmg cosθc

Which of the following statements regarding these equations is not correct?

Answer 3

The value of ms increases proportionally to θ

Question 4

The diagram shows a block of wood resting on an incline. If we wish to use Newton’s second law to determine values for the frictional and the normal forces, we need to choose a coordinate system. On the diagram, the x-axis is parallel to the inclined plane and the y-axis is perpendicular to it. Which of the following statements incorrectly describes why this is the optimal placement of the coordinate system?

Answer 4

Plotting the coordinate system parallel to the inclined plane helps us to visualize the motion of the block, and it eliminates the need to solve for values of the y-axis.

Question 5

Which of the following statements regarding basic frictional problems on inclines is not correct?

Answer 5

The greater the mass of an object, the greater the critical angle will be before it begins to accelerate down an inclined plane

Question 6

The diagram shows a wooden block on an inclined ramp. Which of the following statements regarding this example is correct?

Answer 6

• The block will move down with an acceleration of g sinθm/s^2, assuming there is no friction
• When there is friction, the block remains motionless until the incline reaches a certain angle and then the block accelerates down the ramp.
• The critical angle is the angle that must be reached for the block to accelerate down the ramp when friction is present

Question 7

The diagram shows a block of wood on a ramp. The ramp is slowly being raised, so that θ is increasing. Forces at work on the object include the normal force, N, and the weight of the object, W, and the force of static friction, fs. Which of the following statements regarding this examples is not correct?

Answer 7

The magnitude of static friction depends on the magnitude of the other forces. As θ increases, fs decreases, until the critical angle is reached and the wood block breaks free

Question 8

The equation msmgcosθc = mgsinθc can be rewritten as ms = tanθc. Combining these two equations into one has significant implications. Which of the following statements regarding this equation is correct?

Answer 8

• The mass, m, in the equations cancel. This means that regardless of the mass of the object, the critical angle in the system will always be the same.
• The gravity, g, in the equations cancel. This means that regardless of the gravity present, the critical angle in the system will always be equal.
• The tangent of the critical angle in any similar example gives the value for ms

Question 9

Look at the force diagram for a block of wood resting on an incline and the same force diagram with incomplete components for the weight vectors in the x- and y-directions. Which of the following formulas for calculating Wx and Wy is correct?

Answer 9

Wx = mg sinθ