Which Diagram represents summer?
1 answer:
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The launch velocity is 4.8 m/s
Explanation:
We can solve this problem by applying the law of conservation of energy. In fact, the mechanical energy of the hopper (equal to the sum of the potential energy + the kinetic energy) is conserved. So we can write:
where:
is the initial potential energy, at the bottom
is the initial kinetic energy, at the bottom
is the final potential energy, at the top
is the final kinetic energy, at the top
We can rewrite the equation as:
where:
m is the mass of the hopper
is the acceleration of gravity
is the initial height
u is the launch speed of the hopper
is the maximum altitude reached by the hopper
v = 0 is the final speed (which is zero when the hopper reaches the maximum height)
Solving the equation for u, we find the launch speed of the hopper:
Learn more about kinetic energy and potential energy:
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A) Time needed: 6.24 s
B) Time needed: 2.86 s
Explanation:
A)
In this part, we are told that the power if the engine is constant. The power of the engine is given by
where
W is the work done
t is the time
This means that the power of the engine is proportional to the work done, and therefore, to the kinetic energy of the car:
where m is the mass of the car and v its velocity.
SInce power is constant, we can write:
where:
is the time the car needs to accelerates to
is the time the car needs to accelerate to
Therefore, solving for ,
B)
First of all, we have to calculate the acceleration of the car. We can do it using the following equation:
where:
u = 0 is the initial velocity
is the final velocity
t = 1.40 s is the time elapsed
Substituting, we find the acceleration:
In this part, we are told that the force exerted by the engine is constant: according to Newton's second law, acceleration is proportional to the force,
This means that the acceleration is also constant.
Now we want to find how long the car takes to accelerate to a final velocity of
From an initial velocity of
u = 0
Using again the same suvat equation, and using the acceleration we found previously, we find:
Learn more about accelerated motion:
About power:
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