A motorized lift runs along a stairway inclined at 30^∘. (a) Find the work done in lifting a 75-

step 1 So let us solve the first part of this problem. So the work done by the person will be equals to

A motorized lift runs along a stairway inclined at 30^∘. (a)...

A motorized lift runs along a stairway inclined at $30^{\circ}$. (a) Find the work done in lifting a $75-\mathrm{kg}$ person and $22-\mathrm{kg}$ chair if the track's length is $5.6 \mathrm{~m}$. (b) What power must the motor deliver if the person is to make it from bottom to top in $12 \mathrm{~s} ?$

A motorized lift runs along a stairway inclined at $30^{\circ}$.
(a) Find the work done in lifting a $75-\mathrm{kg}$ person and $22-\mathrm{kg}$ chair if the track's length is $5.6 \mathrm{~m}$. (b) What power must the motor deliver if the person is to make it from bottom to top in $12 \mathrm{~s} ?$

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Key Concepts

Inclined Plane Geometry

Inclined plane geometry involves analyzing the components of forces or displacements in systems with an angle. In problems where objects move along an inclined surface, the vertical displacement is determined by the sine of the inclination angle multiplied by the distance along the plane, linking geometry to physical quantities like work and energy.

Power

Power is the rate at which work is done or energy is transferred, defined as the work performed per unit time. It quantifies how quickly energy is used, and in mechanical scenarios, it is key to understanding the efficiency and performance of machines like motors and lifts.

Work

Work is defined as the energy transferred to an object when a force is applied to move it over a distance. In physics, it is often calculated as the product of the force applied along the direction of displacement and the magnitude of that displacement, embodying the concept of energy transfer in mechanical processes.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When an object is raised to a height, work is done against gravity, which is stored as gravitational potential energy, calculated by multiplying the mass, gravitational acceleration, and the change in vertical height.

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