Question

Consider the system shown in the figure below. BlockA 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/s2
direction	---Select---upward downward

Answer 1

Concepts and reason

The concepts required to solve the given question are the Newton’s second law of motion and the types of forces acting on an object along an inclined plane.

Initially, find an expression for the net force acting on the system using Newton’s second law of motion. Then Substitute the values in the expression. Calculate the coefficient of kinetic friction from the expression. After that, apply Newton’s second law of motion in the case of block A. Write an expression for the net force acting on the block A. Then calculate the magnitude and direction of acceleration by solving the above expression.

Fundamentals

Force may be defined as the sudden push or pull which is capable of changing the direction of the object.

Newton’s second law of motion: It states that the acceleration of an object produced by a net force is directly proportional to the magnitude of net force and inversely proportional to the mass of the object.

Mathematical expression for Newton’s second law is,

Here, F is the force acting on the object, m is the mass and a is the acceleration of the object.

Mass of the object is defined as the “physical property that measures an object’s resistance to acceleration”. Acceleration of the object may be defined as the “rate of change of velocity per unit time”.

Frictional force is the resistive force which tries to oppose the motion of the object. The direction of the frictional force is opposite to that of the direction of motion. Coefficient of kinetic friction becomes more pronounced in the case of surfaces in relative motion. It is the ratio of frictional force to normal force (force perpendicular to the surface).

Mathematical expression for coefficient of kinetic friction is,

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

Weight of the object is the mass times acceleration due to gravity of the object. The expression is given by,

Here, W is the weight of the object, m is the mass and g is the acceleration due to gravity.

(a)

Coefficient of kinetic friction:

Net horizontal force acting on A is,

……(1)

Net horizontal force acting on B is,

From equation (1),

Coefficient of kinetic friction between block A and tabletop is,

Substitute 29 N for 43.2 N for to find .

(b)

Magnitude and direction of acceleration:

Net force acting on the block B is,

……(2)

Net force acting on the block A is,

Substitute for from equation (2) in the above equation.

Substitute for and , for and for in the above equation.

Ans: Part a

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

Part b

Magnitude of acceleration of block B during the downward motion is, and the direction is upwards.