Video Transcript
A body of mass 45 kilograms was placed in a spring balance fixed to the ceiling of an elevator. If the elevator was accelerating downward at 105 centimeters per second squared, what would the apparent weight of a body be? Consider the acceleration due to gravity to be 9.8 meters per second squared and round your answer to two decimal places.
A spring balance does not have a surface that supports a body but rather suspends a body from a spring. In this question, the spring balance is attached to the ceiling of an elevator as shown. As such, the tension of the spring produced by the weight of the body acts equivalently to the reaction force that the surface supporting the body would produce. The only difference between the tension force produced by a spring and the reaction force produced by a surface is the point at which the forces act on the body. A surface reaction force acts at a point below the body, and the spring tension acts at a point above the body. This difference is of no importance for the purposes of this question. As the body that the force acts on has no stated features that distinguish it from a particle, it simply has mass. This mass is equal to 45 kilograms.
We are told in the question that the elevator is accelerating downward at 105 centimeters per second squared. Converting this to standard units, this is equal to 1.05 meters per second squared. Using the formula 𝑤 is equal to 𝑚 multiplied by 𝑔 minus 𝑎, where 𝑤 is the apparent weight of the body, 𝑚 is the mass of the body, 𝑔 is the acceleration due to gravity, and 𝑎 is the acceleration of the lift, we can calculate this apparent weight.
Substituting in our values and noting that the acceleration due to gravity is 9.8 meters per second squared, we have 𝑤 is equal to 45 multiplied by 9.8 minus 1.05. This is equal to 45 multiplied by 8.75, which gives us a final answer of 393.75. As this is already given to two decimal places, we can conclude that the apparent weight of the body is 393.75 newtons.
