Calculating Heat Capacity for Cage Weight of 1000 kg at 9 m/s

[Scarlet_pat]

Homework Statement

in the absense of bearing friction a winding engine would raise a cage weighing 1000 kg at 10m/s, but this is reduced by friction to 9 m/s, how much oil, initially at 20 C is required per second to keep the temperature of the bearing down to 70 C
(specific heat capacity of oil is 2100 J/Kg K , g = 9.81 )

Homework Equations

heat energy = mass x specific heat capacity x change of temperature

The Attempt at a Solution

i personally do not know how to attempt this question, i was trying to see if there is any relationship between velocity and energy, but i couldn't find anything. please .. help

 

[RobL14]

The work done by friction is equal to the energy released as heat. Calculate the work done by friction using conservation of energy, then go from there.

 

[Scarlet_pat]

The work done by friction is equal to the energy released as heat. Calculate the work done by friction using conservation of energy, then go from there.

first of all, thank you very much, but yet still i didnt get the correct answer. therefore i would like to find out if i was in the right direction

1. by using linear motion equation : v^2 = u^2 +2as
solved for S : s = v^2-u^2/2a

when distance is found. i calculated the force = mg

word done by the friction is equal to the heat energy therefore : force = mg x S

since heat energy is found. equation ... Heat energy = m c ( theta temp ) was used
solve for mass
M = heat energy / c ( theta temp.)
am i correct?

 

[Scarlet_pat]

first of all, thank you very much, but yet still i didnt get the correct answer. therefore i would like to find out if i was in the right direction

1. by using linear motion equation : v^2 = u^2 +2as
solved for S : s = v^2-u^2/2a

when distance is found. i calculated the force = mg

word done by the friction is equal to the heat energy therefore : force = mg x S

since heat energy is found. equation ... Heat energy = m c ( theta temp ) was used
solve for mass
M = heat energy / c ( theta temp.)
am i correct?

 

[rwisz]

I would approach this problem by first understanding the concept of heat capacity and how it relates to the specific heat capacity of a substance. Heat capacity is defined as the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius, and it is directly proportional to the mass and specific heat capacity of the substance.

In this problem, we are given the weight of the cage (1000 kg) and the specific heat capacity of the oil (2100 J/kg K). We are also given the initial and final temperatures (20 C and 70 C) and the rate at which the temperature is changing (9 m/s). From this information, we can calculate the heat energy required to keep the bearing at 70 C using the equation:

Heat energy = mass x specific heat capacity x change in temperature

Substituting the given values, we get:

Heat energy = (1000 kg) x (2100 J/kg K) x (70 C - 20 C)

= 420,000,000 J

Next, we need to find the rate at which this heat energy is being produced, which is given by the equation:

Heat energy per second = mass x specific heat capacity x change in temperature per second

In this case, the change in temperature per second is given by the velocity of the cage (9 m/s). So, the heat energy per second is:

Heat energy per second = (1000 kg) x (2100 J/kg K) x (9 m/s)

= 18,900,000 J/s

Finally, we need to find the amount of oil required per second to dissipate this heat energy and maintain the bearing temperature at 70 C. This can be done using the equation:

Mass of oil per second = heat energy per second / specific heat capacity of oil

Substituting the values, we get:

Mass of oil per second = (18,900,000 J/s) / (2100 J/kg K)

= 9,000 kg/s

Therefore, to keep the bearing temperature at 70 C, we would need 9,000 kg of oil per second. This calculation assumes that all the energy produced by friction is absorbed by the oil and does not take into account any other factors such as heat loss to the surroundings.