A block of mass m rests on a rough plane inclined at with the horizontal (Figure).
Question:
A block of mass m rests on a rough plane inclined at θ with the horizontal (Figure). The block is attached to a spring of constant k near the top of the plane. The coefficients of static and kinetic friction between the block and plane are µs and µk, respectively. The spring is slowly pulled upward along the plane until the block starts to move.
(a) Obtain an expression for the extension d of the spring the instant the block moves.
(b) Determine the value of µk such that the block comes to rest just as the spring is in its unstressed condition, i.e., neither extended nor compressed.
Step by Step Answer:
a The force exerted by the spring must equal the sum ...View the full answer
Fundamentals of Ethics for Scientists and Engineers
ISBN: 978-0195134889
1st Edition
Authors: Edmund G. Seebauer, Robert L. Barry
Related Video
Static friction and kinetic friction are two types of friction that occur when two objects are in contact with each other. Static friction is the force that must be overcome to initiate motion between two surfaces that are in contact with each other but are not moving relative to each other. It is caused by the interlocking of rough surfaces at the microscopic level, and it increases as the force pushing the surfaces together increases. Once motion between the surfaces starts, the static friction is no longer present. Kinetic friction, also known as sliding friction, is the force that opposes the motion of two surfaces that are in contact with each other and are moving relative to each other. It is caused by the rubbing of the surfaces against each other and the resistance of the molecules in the surfaces to being moved. Kinetic friction is generally less than static friction, but it can still be a significant force, especially at high speeds. Both static and kinetic friction can be quantified using a coefficient of friction, which is a dimensionless number that represents the ratio of the frictional force between two surfaces to the normal force (the force perpendicular to the surfaces). The coefficient of static friction is typically greater than the coefficient of kinetic friction for a given pair of surfaces, because it takes more force to overcome the interlocking of the surfaces at rest than to maintain motion once it has started.
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