When the mass is expressed in slugs and the acceleration in ft/s^2, you have to use a value of 32.2 (lbm ft)/(lbf s^2) for gc, in order to obtain the force in poundals.

When the mass is expressed in slugs and the acceleration in ft/s^2, you have to use a value of 32.2 (lbm ft)/(lbf s^2) for gc, in order to obtain the force in poundals. When the mass is expressed in lbm and the acceleration in ft/s^2, you have to use a value of 32.2 (lbm ft)/(lbf s^2) for gc, in order to obtain the force in slugs. When the mass is expressed in kgm and the acceleration in m/s^2, you have to use a value of 9.81 (kgm m)/(kgf s^2) for gc, in order to obtain the force in newtons. If a body has a mass of 65 kgm, then its weight is 32.2 kgf. When the mass is expressed in lbm and the acceleration in ft/s^2, you have to use a value of 32.2 (lbm ft)/(lbf s^2) for gc, in order to obtain the force in poundals.

The Correct Answer and Explanation is:

To clarify the scenario you’re describing, it’s all about converting between different units of mass, force, and acceleration in physics. You’re essentially dealing with the concept of weight, which is the force exerted by gravity on an object.

Gravitational Constant (gc)

• gc (gravitational constant) represents the acceleration due to gravity in a specific unit system. It connects mass and force in different unit systems, like the metric system, Imperial system, and others.
• The value of gc depends on whether you’re using slugs, kilograms, or pound-mass (lbm) for mass, and whether you’re working in feet-per-second squared or meters-per-second squared for acceleration.

Unit Systems:

1. Mass in slugs & Acceleration in ft/s²:
   • The force (weight) is expressed in poundals (the unit of force in the foot-pound-second system).
   • In this system, we use the gravitational constant gc = 32.2 (lbm·ft)/(lbf·s²), which is the standard value to calculate the force in poundals.
   The relationship here is based on the fact that 1 poundal is the force that will accelerate a 1 lbm mass by 1 foot per second squared. The formula would be: Force=Mass×Acceleration=65 lbm×32.2 ft/s²\text{Force} = \text{Mass} \times \text{Acceleration} = 65 \, \text{lbm} \times 32.2 \, \text{ft/s²}Force=Mass×Acceleration=65lbm×32.2ft/s²
2. Mass in lbm & Acceleration in ft/s²:
   • When the mass is in pound-mass (lbm) and acceleration in ft/s², you also use gc = 32.2 for converting to poundals (again, the force unit in Imperial).
   • However, the units for force change based on the mass of the object, with the gravitational constant acting as the scaling factor.
3. Mass in kilograms & Acceleration in m/s²:
   • When mass is measured in kilograms and acceleration in meters per second squared (m/s²), you work with the metric system, and the gravitational constant used here is gc = 9.81 (kg·m)/(kgf·s²).
   • The result of this calculation would give you force in newtons (N), the standard unit of force in the metric system.

Example with 65 kg:

• If a body has a mass of 65 kg, we can calculate its weight (force due to gravity) using the gravitational constant for the metric system: Weight=65 kg×9.81 m/s²=637.65 N\text{Weight} = 65 \, \text{kg} \times 9.81 \, \text{m/s²} = 637.65 \, \text{N}Weight=65kg×9.81m/s²=637.65N This means that the weight of a 65 kg mass is 637.65 newtons.

Converting Between Systems:

• If you wanted to convert this to pounds or poundals, you’d need to take into account the differences in unit systems and the appropriate gc values for each. For instance, converting kg to lbm and using the correct gravitational constant would give a different numerical result, but it still represents the same physical force.

In summary:

• 32.2 (lbm·ft)/(lbf·s²) for Imperial units, used for finding force in poundals.
• 9.81 (kg·m)/(kgf·s²) for the metric system, used to find force in newtons.