A 10 kg mass is lifted 5 m with an upward acceleration of 2 m/s^2 (Note: a process diagram is not required for this problem) a) What is the upward force necessary to lift the box? Express your answer in both N and primary units. b) How much energy is required to lift the box? Express your answer in both J and in primary units. c) If this process takes 2.23 seconds, find the average power required to lift the box? Express your answer in both W and primary units, d) Express your answer in part b in terms of kilowatt-hours

a) Newton's Second Law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object.

F=ma

where:

F, the net force [N]
m, mass of the object [kg]
a, acceleration [m/s^2]

If a 10 kg mass is lifted with an upward acceleration of 2 m/s^2, the upward force necessary is:

F=10 [kg]*2[m/s^2]=20 [kgm/s^2]=20 [N]

b) The amount of energy required to lift the box equals the magnitud of work done by the lifting force:

W=FdcosФ

where:

W, work executed [J]
F, net force [N]
d, displacement produced by the force [m]
Ф, angle between the net force and displacemt produced

Thus, the energy required to lift 5 m the mass is:

W=20[N]*5[m]cos0°=100[N.m]=100[kgm^2/s^2]=100[J]

c) To find the average power we use the formula:

P=W/t

where,

P, average power [W]
W, work executed [J]
t, elapsed time [s]

Thus, if the process takes 2,23 seconds the average power is:

P=100[J]/2,23[s]=44,84[J/s]=44,84[kgm^2/s^3]=44,84[W]

d) As 1 kilowatt-hours=3,6*10^6 J, then:

100 [J]*1 [kilowatt-hour]/ 3,6*10^6 [J]=2,778*10^-5 [kilowatt-hours]