A portmanteau of length 1.5 m and height 1 m is carried up stairs by two men, who hold it by t

step 1 First, we draw free body diagram and now join capital G center of gravity and with M that is mid

A portmanteau of length 1.5 m and height 1 m is carried up...

A portmanteau of length $1.5 \mathrm{~m}$ and height $1 \mathrm{~m}$ is carried up stairs by two men, who hold it by the front and back edges of its lower face. If the portmanteau is inclined at $30^{\circ}$ to the horizontal and weighs $100 \mathrm{~kg}$, how much of the weight each man support? (a) $6925 \mathrm{~N}$ and $30.75 \mathrm{~N}$ (b) $6.925 \mathrm{~N}$ and $3075 \mathrm{~N}$ (c) $500 \mathrm{~N}$ and $600 \mathrm{~N}$ (d) $400 \mathrm{~N}$ and $600 \mathrm{~N}$

A portmanteau of length $1.5 \mathrm{~m}$ and height $1 \mathrm{~m}$ is carried up stairs by two men, who hold it by the front and back edges of its lower face. If the portmanteau is inclined at $30^{\circ}$ to the horizontal and weighs $100 \mathrm{~kg}$, how much of the weight each man support?
(a) $6925 \mathrm{~N}$ and $30.75 \mathrm{~N}$
(b) $6.925 \mathrm{~N}$ and $3075 \mathrm{~N}$
(c) $500 \mathrm{~N}$ and $600 \mathrm{~N}$
(d) $400 \mathrm{~N}$ and $600 \mathrm{~N}$

Key Concepts

Static Equilibrium

This concept refers to a state in which an object remains at rest because the total forces and total torques (moments) acting on it are balanced. It is crucial in analyzing the problem because the portmanteau on the stairs is not accelerating, and the forces applied by the two men must exactly counteract the gravitational force and produce no net torque.

Torque (Moment)

Torque or moment is the force that causes an object to rotate about an axis. It is calculated as the product of the force and its moment arm (the perpendicular distance from the line of force to the pivot point). In the context of this problem, determining the distribution of the weight supported by each man involves calculating torques about a chosen pivot point.

Center of Mass

The center of mass is the point at which the total mass of an object can be considered to be concentrated for the purpose of analyzing its motion under gravity. Recognizing where the center of mass is located helps in setting up the torque equilibrium equations, as gravitational force can be assumed to act through this point.

Lever Arms

Lever arms are the perpendicular distances from the line of action of a force to the pivot or fulcrum. They are critical in computing the torque produced by each force. In problems like this, differences in lever arms determine how force is distributed between the two supports.

Inclined Plane Mechanics

This concept involves analyzing forces acting on bodies that are on an inclined surface. Decomposing the weight and understanding the geometry of the setup, such as the angles of inclination, are necessary for correctly resolving forces parallel and perpendicular to the incline, which in turn impacts the computation of torques and equilibrium conditions.

Transcript

Please give Ace some feedback