Answer:
The amount of kilograms of ice at -20.0°C that must be dropped into the water to make the final temperature of the system 40.0°C = 0.0674 kg
Explanation:
Heat gained by ice in taking the total temperature to 40°C = Heat lost by the water
Total Heat gained by ice = Heat used by ice to move from -20°C to 0°C + Heat used to melt at 0°C + Heat used to reach 40°C from 0°C
To do this, we require the specific heat capacity of ice, latent heat of ice and the specific heat capacity of water. All will be obtained from literature.
Specific heat capacity of ice = Cᵢ = 2108 J/kg.°C
Latent heat of ice = L = 334000 J/kg
Specific heat capacity of water = C = 4186 J/kg.°C
Heat gained by ice in taking the total temperature to 40°C = mCᵢ ΔT + mL + mC ΔT = m(2108)(0 - (-20)) + m(334000) + m(4186)(40 - 0) = 42160m + 334000m + 167440m = 543600 m
Heat lost by water = mC ΔT = 0.25 (4186)(75 - 40) = 36627.5 J
543600 m = 36627.5
m = 0.0674 kg = 67.4 g of ice.
Answer:
Time period, 
Explanation:
Given that,
The quartz crystal used in an electric watch vibrates with a frequency of 32,768 Hz, f = 32768 Hz
We need to find the period of the crystal's motion. The relationship between the frequency and the time period is given by :

T is the time period of the crystal's motion.
Time period is given by :

So, the time period of the crystal's motion is
. Hence, this is the required solution.
To solve this problem we will apply the concepts related to the balance of forces. We will decompose the forces in the vertical and horizontal sense, and at the same time, we will perform summation of torques to eliminate some variables and obtain a system of equations that allow us to obtain the angle.
The forces in the vertical direction would be,



The forces in the horizontal direction would be,



The sum of Torques at equilibrium,




The maximum friction force would be equivalent to the coefficient of friction by the person, but at the same time to the expression previously found, therefore


Replacing,


Therefore the minimum angle that the person can reach is 46.9°
Answer:
The velocity of the ship relative to the earth V = 9.05 
Explanation:
The local ocean current is = 1.52 m/s
Direction
= 40°
Velocity component in X - direction
= 1.52
°
= 1.164 
Velocity component in Y - direction
= 8 + 1.52
°
= 8.97 
The velocity of the ship relative to the earth

Put the values of
and
we get,
⇒ 
⇒ V = 9.05 
This is the velocity of the ship relative to the earth.
Answer:

Explanation:
As we know that electric field due to infinite line charge distribution at some distance from it is given as

now we need to find the electric field at mid point of two wires
So here we need to add the field due to two wires as they are oppositely charged
Now we will have

now plug in all data



now we have


