Question

Constants

1. A 14.6 g bullet traveling horizontally at 865 m/s passes through a tank containing 14.0 kg of water and emerges with a speed of 534 m/s .

What is the maximum temperature increase that the water could have as a result of this event?

2. A copper pot with a mass of 0.525 kg contains 0.155 kg of water, and both are at a temperature of 23.0 ∘C . A 0.270 kgblock of iron at 86.5 ∘C is dropped into the pot.

Find the final temperature of the system, assuming no heat loss to the surroundings.?

3.A thirsty nurse cools a 2.40 L bottle of a soft drink (mostly water) by pouring it into a large aluminum mug of mass 0.247 kg and adding 0.122 kg of ice initially at -15.2 ∘C. If the soft drink and mug are initially at 20.9 ∘C, what is the final temperature of the system, assuming no heat losses?

4.The icecaps of Greenland and Antarctica contain about 1.75 % of the total water (by mass) on the earth's surface; the oceans contain about 97.5 % , and the other 0.75 % is mainly groundwater. Suppose the icecaps, currently at an average temperature of about -31 ∘C, somehow slid into the ocean and melted.

What would be the resulting temperature decrease of the ocean? Assume that the average temperature of ocean water is currently 5.00 ∘C. ?

Answer 1

here,

1)

the mass of bullet , m1 = 14.6 g = 0.0146 kg

mass of water , m2 = 14 kg

the initial speed of bullet , u1 = 865 m/s

final speed of bullet , v1 = 534 m/s

let the speed of block be v

using conservation of momentum

m1 * u1 = m1 * v1 + m2 * v

0.0146 * ( 865 - 534) = 14 * v

v = 0.345 m/s

let the change in temperature be Tf

using conservation of energy

(0.5 * m1 * u^2 - (0.5 * m1 * v1^2 + 0.5 * m2 * v^2)) = m2 * Cw * dT

(0.5 * 0.0146 * 865^2 - (0.5 * 0.0146 * 534^2 + 0.5 * 14 * 0.345^2)) = 14 * 4186 * dT

solving for dT

dT = 0.058 degree C

the change in temperature is 0.058 degree C