A worker pushes horizontally on a 35 kg crate with a force of magnitude 110 N. The coefficient

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

A worker pushes horizontally on a $35 \mathrm{~kg}$ crate with a force of magnitude $110 \mathrm{~N}$. The coefficient of static friction between the crate and the floor is $0.37$. (a) What is the frictional force on the crate from the floor? (b) What is the maximum magnitude $f_{\max }^{\text {stat }}$ of the static frictional force under the circumstances? (c) Does the crate move? (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 $110 \mathrm{~N}$ 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

Force Decomposition and Net Force

Force decomposition involves breaking a force into its horizontal and vertical components, especially when forces are applied at an angle. Combining these components properly is necessary to evaluate the net force acting on an object. This concept is important in determining whether the total horizontal force can overcome static friction or if adjustments to vertical forces are needed to facilitate motion.

Normal Force

The normal force is the force exerted by a surface perpendicular to the object resting on it. It usually equals the object's weight when on a horizontal surface; however, it can change if additional vertical forces, such as an upward pull, are applied. Understanding the normal force is essential as it directly influences frictional forces.

Maximum Static Friction

Maximum static friction refers to the highest possible magnitude of static friction that can develop between two surfaces before motion begins. It is calculated by multiplying the coefficient of static friction by the normal force. Recognizing this limit is crucial in determining whether an applied force is sufficient to initiate movement.

Static Friction

Static friction is the resistive force that prevents two surfaces from sliding past each other when a force is applied. It adjusts in magnitude to match the applied force up to a maximum value, which must be exceeded for motion to commence. This concept is central in understanding why objects at rest do not move until the applied force overcomes this maximum frictional force.

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