Question

An elevator is rising at constant speed. Consider the following statements: I. the upward cable force is constant II. the kinetic energy of the elevator is constant III. the gravitational potential energy of the Earth-elevator system is constant IV. the acceleration of the elevator is zero V. the mechanical energy of the Earth-elevator system is constan

Answer 1

I, II & IV are true

III & V are not true

Step-by-step explanation:

TRUE STATEMENTS

I) At constant speed, constant mass and given that acceleration due to gravity is also constant, the upward cable force is constant.

II) K.E is given by
`(1)/(2) mv^(2)`

at constant mass and constant velocity (speed), the K.E of the elevator is constant.

IV) Acceleration is given by change in speed over a given time, i a system where the speed is constant i.e. initial speed = final speed, change in speed is zero (0) and as such, acceleration is zero.

FALSE STATEMENTS

III) There is constant gravitational work done to resist the upward movement of the system and the energy expended for this work increases as the elevator goes higher (P.E = mgh), as such, gravitational P.E is not constant.

V) The elevator system has a constant Kinetic energy, however the potential energy increases with height and as such, the mechanical energy of the system is not constant.

Answer 2

I True

II True

III False

IV True

V False

Step-by-step explanation:

I. the upward cable force is constant

True. As the elevator is rising at constant speed. According to Newton's first law, the net force acting on it must be zero. Vertically there are 2 forces at play here: gravity and the cable tension. They are equal and opposite. Since mass is unchanged, gravity is unchanged, so is the tension force.

II. the kinetic energy of the elevator is constant

True. Since
`E_k = (mv^2)/(2)`. Mass is constant, speed is constant. Then the kinetic energy must be constant.

III. the gravitational potential energy of the Earth-elevator system is constant

False. As the elevator is rising, its height with respect to a reference system is increasing. and
`E_p = mgh`. So the gravitational potential energy must be changing too.

IV. the acceleration of the elevator is zero

True. Since speed is constant. And acceleration is change of speed over time. Acceleration must be 0 here.

V. the mechanical energy of the Earth-elevator system is constant

False as the elevator is withdrawing energy from external and converting to potential energy for it to rise. Total Mechanical energy must be rising as well.