Answer:
t=1.4hours
Explanation:
The half life is 1hour
At t=0 he has a mass of 4kg
So he want it to be 1kg, so that his weapon can work.
Applying the exponential function of decay
M=Cexp(-kt)
Where,
M is the mass at any time
C is a constant of integration
k is the rate of decay
Given that it has an half life of 1 hours.
Then k is 1
At t =0 the mass is 4kg
Therefore
4=Cexp(0)
C=4
M=4exp(-kt)
Since rate of decay is 1, then k=1
M=4exp(-t)
We need to find t at M=1kg
1=4exp(-t)
1=4exp(-t)
1/4=exp(-t)
0.25=exp(-t)
Take In of both sides
In(0.25)=-t
-1.3863=-t
Then, t=1.386hour
Then it will take about 1.4 hours to get to 1kg.
Answer:
801.1 kJ
Explanation:
The ice increases in temperature from -20 °C to 0 °C and then melts at 0 °C.
The heat required to raise the ice to 0 °C is Q₁ = mc₁Δθ₁ where m = mass of ice = 1 kg, c₁ = specific heat capacity of ice = 2108 J/kg°C and Δθ₁ = temperature change. Q₁ = 1 kg × 2108 J/kg°C × (0 - (-20))°C = 2108 J/kg°C × 20 °C = 4216 J
The latent heat required to melt the ice is Q₂ = mL₁ where L₁ = specific latent heat of fusion of ice = 336000 J/kg. Q₁ = 1 kg × 336000 J/kg = 336000 J
The heat required to raise the water to 100 °C is Q₃ = mc₂Δθ₂ where m = mass of ice = 1 kg, c₂ = specific heat capacity of water = 4187 J/kg°C and Δθ₂ = temperature change. Q₃ = 1 kg × 4187 J/kg°C × (100 - 0)°C = 4187 J/kg°C × 100 °C = 418700 J
The latent heat required to convert the water to steam is Q₄ = mL₂ where L = specific latent heat of vapourisation of water = 2260 J/kg. Q₄ = 1 kg × 2260 J/kg = 2260 J
The heat required to raise the steam to 120 °C is Q₅ = mc₃Δθ₃ where m = mass of ice = 1 kg, c₃ = specific heat capacity of steam = 1996 J/kg°C and Δθ₃ = temperature change. Q₃ = 1 kg × 1996 J/kg°C × (120 - 100)°C = 1996 J/kg°C × 20 °C = 39920 J
The total amount of heat Q = Q₁ + Q₂ + Q₃ + Q₄ + Q₅ = 4216 J + 336000 J
+ 418700 J + 2260 J + 39920 J = 801096 J ≅ 801.1 kJ
Answer:
Wp = 1,272 J
Wf = -940.8 J
Wn = 0
Wg = 0
Explanation:
- Applying the definition of work, as the product of the component of the force applied, along the direction of the displacement, times the displacement, we find that due to the normal force is always perpendicular to the surface, it does no work, as it has not a component in the direction of the displacement, so Wn = 0.
- As the weight goes directly downward, it has no component in the direction of the displacement either, so Wg = 0.
- We can get the work done by the force applied P, simply as follows:
- Finally, we have the work done by the force of friction that always opposes to the displacement, so it has negative sign.
- The frictional force , can be written as follows:
where μk = coefficient of kinetic friction = 0.24
Fn = Normal Force
- In this case, since the surface is level and horizontal, and there is no acceleration of the box in the vertical direction, this means that the normal force (in magnitude) must be equal to the weight:
- Fn = m*g = 50 kg * 9.8 m/s2 = 490 N
- Replacing these values in (2), we get:
- Applying the definition of work, we can get the work done by the frictional force, as follows:
<h2>
Answer:</h2>
The distance will be 1800 m
<h2>
Explanation</h2>
As in question
Time = 15 min
Time = 15 x 60 sec = 900 sec
Speed = 2 m/s
We know that
So, the answer is 1800 m
