An electric motor M is used to reel in cable and hoist a...

An electric motor $M$ is used to reel in cable and hoist a bicycle into the ceiling space of a garage. Pulleys are fastened to the bicycle frame with hooks at locations $A$ and $B$, and the motor can reel in cable at a steady rate of 12 in./sec. At this rate, how long will it take to hoist the bicycle 5 feet into the air? Assume that the bicycle remains level.

An electric motor $M$ is used to reel in cable and
hoist a bicycle into the ceiling space of a garage. Pulleys are fastened to the bicycle frame with hooks at locations $A$ and $B$, and the motor can reel in cable at a steady rate of 12 in./sec. At this rate, how long will it take to hoist the bicycle 5 feet into the air? Assume that the bicycle remains level.

Key Concepts

Unit Conversion

Unit conversion is a critical concept in many physics and engineering problems, ensuring that all lengths, speeds, and other quantities are expressed in consistent units. This makes mathematical operations, such as computing time or distance, straightforward and error?free.

Pulley Systems and Mechanical Advantage

A key idea in systems that use pulleys is understanding how forces and movements are distributed. When a load is supported by multiple cable segments via pulleys, the distance pulled in one cable may not correspond directly to the distance the load moves, often resulting in a mechanical advantage that affects the effective motion.

Kinematics: Distance, Speed, and Time

Kinematics involves the relationship between distance, speed, and time. In cases with a constant rate of movement, the time required to cover a specific distance can be calculated directly using the equation time = distance ÷ speed, which is fundamental in solving these types of problems.

Load Hoisting Dynamics

Analyzing how a load is hoisted involves understanding the dynamics of the lifting system. In setups where multiple cables or points of support are involved and the load is kept level, there is a specific relationship between the amount of cable reeled in and the actual vertical displacement of the load, which is an important factor in correctly determining the time required to lift the load.

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