7 In Fig. 6-23, a force acts on a block weighing 45 N.The...

7 In Fig. 6-23, a force acts on a block weighing 45 N.The block is initially at rest on a plane inclined at angle u 15 to the horizontal. The positive direction of the x axis is up the plane. Between block and plane, the coefficient of static friction is ms 0.50 and the coefficient of kinetic friction is mk 0.34. In unit-vector notation, what is the frictional force on the block from the plane when is (a) (5.0 N) , (b) (8.0 N) , and (c) (15 N) ?

7 In Fig. 6-23, a force acts on a block weighing 45 N.The block
is initially at rest on a plane inclined at angle u 15 to the horizontal. The positive direction of the x axis is up the plane. Between
block and plane, the coefficient of static friction is ms 0.50 and
the coefficient of kinetic friction
is mk 0.34. In unit-vector notation, what is the frictional force
on the block from the plane when
is (a) (5.0 N) , (b) (8.0 N) ,
and (c) (15 N) ?

Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It can adjust its magnitude to counteract a small applied force up to a certain maximum value, which is proportional to the normal force and the coefficient of static friction. Its direction always opposes the intended motion, ensuring that the objects remain at rest until a threshold is passed.

Kinetic Friction

Kinetic friction is the resistive force that acts between surfaces in relative motion. Once an object starts sliding, kinetic friction comes into play and typically has a constant magnitude given by the product of the kinetic friction coefficient and the normal force. Its magnitude is usually lower than the maximum static friction force, and it always acts opposite to the direction of the object's movement.

Inclined Plane Analysis

Inclined plane analysis involves examining the forces acting on an object placed on a sloped surface. The weight of the object is resolved into components parallel and perpendicular to the plane. The normal force balances the perpendicular component, while friction and any additional applied forces interact with the parallel component to determine the object’s motion or equilibrium.

Unit Vector Notation

Unit vector notation is a mathematical representation used to denote directions in space by employing unit vectors. Each unit vector has a magnitude of one and points along a specific coordinate axis. Representing forces using unit vectors provides clarity on both the magnitude and direction, which is essential for vector addition and resolving forces along inclined planes.

Transcript

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