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When you weigh yourself on solid ground, your weight is 139 lb. In an elevator, your apparent weight is 119 lb. What is the magnitude of the elevator's acceleration?

Answer :

To determine the elevator's acceleration, we use Newton's second law of motion and the apparent weight difference. By calculating the mass from the actual weight and applying the formula for net force, we find the elevator's acceleration.

When you weigh 139 lb on solid ground, your weight is the force exerted by Earth's gravity on your body. If in an elevator, your apparent weight is 119 lb, this indicates that the force exerted by the scale reading is less than the force of gravity. The difference in weight reading can be attributed to the elevator's acceleration.

To find the magnitude of the elevator's acceleration, we use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration (Fnet = ma). The apparent weight is the actual force the scale reads, which in this case acts upwards, while the real weight acts downwards. We can express this difference as a = (w - wapp)/m, where w is the real weight, wapp is the apparent weight, and m is the mass.

Using the given weights and assuming Earth's gravitational acceleration is 9.80 m/s², we can calculate the mass as m = w/g. Substituting the known values, m = 139 lb / (9.80 m/s²) and then converting pounds to kilograms (1 lb = 0.453592 kg), we find m ≈ 63.05 kg. Now we can find the acceleration of the elevator as a = (w - wapp) / m = (139 lb - 119 lb) * 9.80 m/s² / (63.05 kg * 9.80 m/s²).

After converting 139 lb and 119 lb to kilograms and calculating, we get a value for the acceleration. This resulting acceleration is the elevator's acceleration. Remember to keep units consistent when performing these types of calculations.

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