Question

An elevator is supported by a cable and moving downward through the elevator shaft and speeding up. How does the upward tension force compare to the downward force of gravity?a)The tension force and the force of gravity are of equal strength.b)The upward tension force is stronger than the downward force of gravity.c)The downward force of gravity is stronger than the upward tension force.

Answer 1

Step-by-step explanation

The second Newton´s law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object, in other words the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force

`\begin{gathered} F=ma \\ where\text{ F is the force} \\ m\text{ is the mass} \\ a\text{ is the acceleration} \end{gathered}`

Step 1

Free body diagram

so, in x direction we have

`\begin{gathered} Tension\text{ Force+mg= ma} \\ T=m(g-a) \end{gathered}`

if we assume the elevator moving downwatds, the acceleration is postivive in that direction, so

`\begin{gathered} Temsion\text{ force=ma+mg} \\ tension\text{ force= m\lparen a+g\rparen} \\ \end{gathered}`

c)The downward force of gravity is stronger than the upward tension force.