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1 answer:
The amount of heat needed to increase the temperature of a substance by 
is given by
where
m is the mass of the substance
Cs is the specific heat capacity of the substance
is the increase of temperature of the substance
If we plug the data of the problem into the formula, we find
and this is the amount of heat needed to bring 12.5 g of aluminium from 20 degrees to 100 degrees.
where
m is the mass of the substance
Cs is the specific heat capacity of the substance
If we plug the data of the problem into the formula, we find
and this is the amount of heat needed to bring 12.5 g of aluminium from 20 degrees to 100 degrees.
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The horizontal force applied to the block is approximately 1,420.84 N
The known parameters;
The mass of the block, w₁ = 400 kg
The orientation of the surface on which the block rest, w₁ = Horizontal
The mass of the block placed on top of the 400 kg block, w₂ = 100 kg
The length of the string to which the block w₂ is attached, l = 6 m
The coefficient of friction between the surface, μ = 0.25
The state of the system of blocks and applied force = Equilibrium
Strategy;
Calculate the forces acting on the blocks and string
The weight of the block, W₁ = 400 kg × 9.81 m/s² = 3,924 N
The weight of the block, W₂ = 100 kg × 9.81 m/s² = 981 N
Let <em>T</em> represent the tension in the string
The upward force from the string = T × sin(θ)
sin(θ) = √(6² - 5²)/6
Therefore;
The upward force from the string = T×√(6² - 5²)/6
The frictional force = (W₂ - The upward force from the string) × μ
The frictional force, = (981 - T×√(6² - 5²)/6) × 0.25
The tension in the string, T = × cos(θ)
∴ T = (981 - T×√(6² - 5²)/6) × 0.25 × 5/6
Solving, we get;
The frictional force on the block W₂, ≈ 219.92 N
Therefore;
The force acting the block w₁, due to w₂ = 219.92/0.25 ≈ 879.68
The total normal force acting on the ground, N = W₁ +
The frictional force from the ground, = N×μ +
= P
Where;
P = The horizontal force applied to the block
P = (W₁ + ) × μ +
Therefore;
P = (3,924 + 879.68) × 0.25 + 219.92 ≈ 1,420.84
The horizontal force applied to the block, P ≈ 1,420.84 N
Learn more about friction force here;
Answer:
<em>a. Angle= 28.82°</em>
<em>b. Approved. He will get cold but he should be able to make it across</em>
Explanation:
Velocity Vector
The velocity is a physical quantity that measures how fast or slow at a particular direction some object is moving. It must be expressed as a vector with both a magnitude and direction. If the object is confined to move in one direction, then we can use the speed as the scalar (magnitude only) equivalent of the velocity.
a.
The explorer wants to swim across a river to his campsite, as shown in the image below. The river has a velocity vr and the explorer can swim at ve in still water. If he swam directly to the campsite, he would end up in a point below it because the river would push him down. He must swim with a velocity such that he overcomes the stream but he advances to its objective. Let's call the angle he must swim at respect to the shoreline to achieve his goal. The explorer's velocity can be decomposed in its rectangular components vx and vy. To overcome the river's velocity:
We can compute the vertical component of the explorer's velocity as
Thus
Solving for
Then we have the angle is
b.
The horizontal component of the explorer's velocity is
This is the real velocity the explorer is having directly to the campsite
Knowing that
Solving for t
Calculating the time it takes the explorer to cross the river
Since this value is less than the limit value of hypothermia (300 sec), the decision is
Approved. He will get cold but he should be able to make it across
