Marc attaches a falling 500-kg object with a rope through a pulley to a paddle wheel shaft.He places the system in a well-insulated tank holding 25 kg of water.When the object falls,it causes the paddle wheel to rotate and churn the water.If the object falls a vertical distance of 100 m at constant speed,what is the temperature change of the water? (1 kcal = 4 186 J,the specific heat of water is 4 186 J/kg*$\degree$C,and g = 9.8 m/s²) A)19 600 C $\degree$ B)4 700 C $\degree$ C)4.7 C $\degree$ D)0.8 C $\degree$

Question

Quizplus · Accepted Answer

The potential energy that the object loses as it falls is converted by the paddle wheel to kinetic energy and then transferred to the water, increasing its temperature. The amount of energy transferred to the water can be calculated as follows:

Potential energy lost by object = mgh
= 500 kg x 9.8 m/s^2 x 100 m
= 490,000 J

This energy is transferred to the water, so:

Energy transferred to water = mwater x cwater x ΔT

where mwater is the mass of the water, cwater is the specific heat of water, and ΔT is the temperature change.

Solving for ΔT:

ΔT = (energy transferred to water) / (mwater x cwater)
= (490,000 J) / (25 kg x 4,186 J/kgC)
= 4.7 C

Converting to Fahrenheit:

ΔT = 4.7 C x 1.8 + 32
= 42.3 F

Therefore, the answer is C: 4.7 CF1F1F1S1F1F1F10.

Marc Attaches a Falling 500-Kg Object with a Rope Through °\degree°

Marc Attaches a Falling 500-Kg Object with a Rope Through $\degree$