Takumi works in his yard for 45 minutes each Saturday. He works in the morning, and he wears sunscreen and a hat each time he wo
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a) 893 N
b) 8.5 m/s
c) 3816 W
d) 69780 J
e) 8030 W
Explanation:
a)
The net force acting on Bolt during the acceleration phase can be written using Newton's second law of motion:
where
m is Bolt's mass
a is the acceleration
In the first 0.890 s of motion, we have
m = 94.0 kg (Bolt's mass)
(acceleration)
So, the net force is
And according to Newton's third law of motion, this force is equivalent to the force exerted by Bolt on the ground (because they form an action-reaction pair).
b)
Since Bolt's motion is a uniformly accelerated motion, we can find his final speed by using the following suvat equation:
where
v is the final speed
u is the initial speed
a is the acceleration
t is the time
In the first phase of Bolt's race we have:
u = 0 m/s (he starts from rest)
(acceleration)
t = 0.890 s (duration of the first phase)
Solving for v,
c)
First of all, we can calculate the work done by Bolt to accelerate to a speed of
v = 8.5 m/s
According to the work-energy theorem, the work done is equal to the change in kinetic energy, so
where
m = 94.0 kg is Bolt's mass
v = 8.5 m/s is Bolt's final speed after the first phase
is the initial kinetic energy
So the work done is
The power expended is given by
where
t = 0.890 s is the time elapsed
Substituting,
d)
First of all, we need to find what is the average force exerted by Bolt during the remaining 8.69 s of motion.
In the first 0.890 s, the force exerted was
We know that the average force for the whole race is
Which can be rewritten as
And solving for , we find the average force exerted by Bolt on the ground during the second phase:
The net force exerted by Bolt during the second phase can be written as
(1)
where D is the air drag.
The net force can also be rewritten as
where
is the acceleration in the second phase, with
u = 8.5 m/s is the initial speed
v = 12.4 m/s is the final speed
t = 8.69 t is the time elapsed
Substituting,
So we can now find the average drag force from (1):
So the increase in Bolt's internal energy is just equal to the work done by the drag force, so:
where
d is Bolt's displacement in the second part, which can be found by using suvat equation:
And so,
e)
The power that Bolt must expend just to voercome the drag force is given by
where
is the increase in internal energy due to the air drag
t is the time elapsed
Here we have:
t = 8.69 s is the time elapsed
Substituting,
And we see that it is about twice larger than the power calculated in part c.
When the temperature of 0.50 kg of water decreases by 22 °C, the energy transferred to the surroundings from the water is -46.2 kJ.
A sample of 0.50 kg of water boils (reaches 100 °C). After a while, its temperature decreases by 22 °C.
We can calculate the energy transferred to the surroundings from the water in the form of heat (Q) using the following expression.
where,
- c: specific heat capacity of water
- m: mass of water
- ΔT: change in the temperature
When the temperature of 0.50 kg of water decreases by 22 °C, the energy transferred to the surroundings from the water is -46.2 kJ.
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