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Consider the system shown in the figure below. Block*A* weighs 43.2 N and block *B* weighs 29.0 N. Once block *B* is set into downward motion, it descends at a constant

speed.

(a) Calculate the coefficient of kinetic friction between block *A* and the tabletop.

(b) A cat, also of weight 43.2 N, falls asleep on top of block *A*. If block *B* is now set into downward motion, what

is its acceleration?

magnitude | m/s^{2} |

direction | —Select—upward downward |

To solve the question, you will need to know the Newton’s Second Law of Motion and the types forces that act on objects along inclined planes.

First, use Newton’s second law to find the expression that describes the net force acting upon the system. Next, substitute the values from the expression. From the expression, calculate the coefficient of kinetic friction. Apply Newton’s second law for motion to block A. Find the net force acting upon block A. Next, solve the above expression to calculate the magnitude of acceleration.

Force can be described as a sudden push or pull that is capable of changing the object’s direction.

Newton’s second lawof motion: It states that an object will accelerate if it encounters a net force. However, the net force magnitude is directly proportional and the object’s mass is inversely proportional.The mathematical expression of Newton’s second law,

Frefers to the force that acts on an object,Mthe mass, andAthe acceleration of the object.The object’s mass is the “physical property that measures its resistance to acceleration”. Acceleration can be described as the rate of change in velocity per unit of time.

The resistive force that attempts to stop the object’s motion is called frictional force. The frictional force’s direction is opposite that of the object’s motion. The coefficient of kinetic friction is more prominent when surfaces are in relative motion. It is the ratio frictional force to normal force (force perpendicular the surface).

The mathematical expression for coefficients of kinetic friction is:

refers to the coefficient of kinetic friction. represents the frictional force, the normal force.

The object’s weight is its mass multiplied by the acceleration caused by gravity. This expression is given by

Wrefers to the object’s weight,Mrefers to its mass, andGindicates the acceleration caused by gravity.(

a)Kinetic friction coefficient:The net horizontal force acting on A,

……(1)

The net horizontal force acting on B,

In equation (1),

The coefficient of kinetic friction is the difference between block A (tabletop) and block B (tabletop).

Substitute 29 N for to find .

(

b)Magnitude and direction for acceleration:

The block B is being occupied by the net force

……(2)

The block A block is being occupied by net force

Substitute HTMLmediaTag18$ to from equation (2).

Substitute to or , and to . is for .

Ans: Part A

The coefficient of kinetic friction is 0.671 between block A, and tabletop.

Part b

The magnitude of acceleration of block A during the downward motion of is , and the direction of the upward motion is .