Question

A. Suppose a 10kg object as a total energy of 500J. If all of this energy is kinetic energy, how fast is the object moving? (I got 10 m/s) Is this correct?

B. Assume now that the same object has only gravitational potential energy. If the object is on Earth, how high up is it? (I got 5.1 m, is this correct?)

C. According to conservation of energy, the object must have the same TOTAL energy (kinetic plus potential) at all times. When the object is 2m off of the ground, how fast it moving?

D. Using the same concept, how high up is the object when it's traveling with a velocity of 6m/s?

Answer 1

Solution:

Given,

m - 10 kg, E = 500 J and We take acceleration due to gravity g = 9.81 m/s².

A)

All the energy is K.E,

K.E = 1/2 mv² = 500

v² = 500*2/10

v = 10 m/s.

B)

All the energy is P.E from the earth,

P;E = mgh = 500

h = 500/[9.81*10]

h = 5.1 m.

C)

Given its off the ground,

Total energy is = 500 J

K.E + P.E = 500 J

K.E = 500 - mgh = 500 - [10*9.81*2]

1/2 mv² = 303.8

v² = 303.8*2/10

v = 7.795

= 7.8 m/s.

D)

Given its off the ground,

Total energy is = 500 J

K.E + P.E = 500 J.

P.E = 500 - 0.5mv² = 500 - [0.5*10*6²]

mgh = 320

h = 320/10*9.81

h = 3.262

= 3.3 m.

I hope you understood the problem and got your answers, If yes rate me!! or else comment for a better solutions.