A worker pushes horizontally on a 35 kg crate with a force...

A worker pushes horizontally on a 35 kg crate with a force of magnitude 110 N.The coefficient of static friction between the crate and the floor is 0.37. (a) What is the value of fs,max under the circumstances? (b) Does the crate move? (c) What is the frictional force on the crate from the floor? (d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the first worker’s 110 N push to move the crate? (e) If, instead, the second worker pulls horizontally to help out, what is the least pull that will get the crate moving?

A worker pushes horizontally on a 35 kg crate
with a force of magnitude 110 N.The coefficient of
static friction between the crate and the floor is
0.37. (a) What is the value of fs,max under the circumstances? (b) Does the crate move? (c) What is
the frictional force on the crate from the floor?
(d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the
least vertical pull that will allow the first worker’s 110 N push to
move the crate? (e) If, instead, the second worker pulls horizontally
to help out, what is the least pull that will get the crate moving?

Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces. It is quantified by the equation fs,max = ?s × N, where ?s is the coefficient of static friction and N is the normal force. It determines whether an applied force is sufficient to overcome the frictional resistance and initiate motion.

Normal Force

The normal force is the perpendicular force exerted by a surface on an object in contact with it. In problems involving friction, the normal force plays a critical role since it directly influences the maximum static friction. It is typically equal to the weight of the object, but can be altered by additional vertical forces, such as an upward or downward pull.

Equilibrium Conditions

Equilibrium conditions refer to the state where all forces acting on an object balance each other such that there is no net force and hence no acceleration. In the context of overcoming static friction, the applied force must exceed the maximum static friction for motion to commence.

Force Decomposition

Force decomposition involves breaking down forces into components, usually horizontal and vertical, to analyze their effects independently. This is essential when forces act at angles or when additional forces modify the normal force. Understanding how to decompose forces helps in accurately assessing the net force in each direction.

Effect of Vertical Assistance on Friction

Applying a vertical force, such as an upward pull, can reduce the normal force acting on an object. Since the maximum static friction is proportional to the normal force, reducing it decreases the threshold force needed to overcome friction and initiate movement. This concept is key when considering strategies to assist in moving objects that are otherwise difficult to slide.

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