The work done on the puck is 96 J
Explanation:
According to the work-energy theorem, the work done on the hockey puck is equal to the change in kinetic energy of the puck.
Mathematically:
where
is the final kinetic energy of the puck, with
m = 2 kg being the mass of the puck
v = 10 m/s is the final speed
is the initial kinetic energy of the puck, with
u = 2 m/s being the initial speed of the puck
Substituting numbers into the equation, we find the work done by the player on the puck:
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Answer:
When air resistance equals the weight of an object, the object has reached free fall.
Explanation:
- When an object has only force acting on it as gravity then, it experiences free fall.
- During free fall all the forces except gravity is balanced by one another.
- In the question, object's weight is balanced by air resistance so it is in the state of free fall.
- At the null point of free fall, object experiences weightlessness i.e. it feels like object is not attracted by any force.
From the given equation we can deduce what changes will occur if the frequency of the sound is doubled
V= f (λ)
Speed = frequency. Wavelength
When the frequency is doubled, speed will not change. Because speed depends on factors like temperature, air pressure, density of the gas. Since all these factors are unchanged thus speed will remain unchanged
Frequency is the number of waves produced per second. Frequency and wavelength are inversely proportional .Thus, if the frequency is doubled the wavelength would be halved.
Solution :
Frequency may be defined as the number of observation or number of waves that is taken in per unit time. The unit of frequency is Hertz or Hz.
It is given that :
Successive harmonic frequencies, f = 52.2 Hz
and f' = 60.9 Hz
Therefore, fundamental frequency, F = f' - f
F = 60.9 - 52.2
F = 8.7 Hz
Therefore the string which is fixed at both the ends forms all the harmonics.
To answer this problem, we will use the equations of motions.
Part (a):
For the ball to start falling back to the ground, it has to reach its highest position where its final velocity will be zero.
The equation that we will use here is:
v = u + at where
v is the final velocity = 0 m/sec
u is the initial velocity = 160 m/sec
a is acceleration due to gravity = -9.8 m/sec^2 (the negative sign is because the ball is moving upwards, thus, its moving against gravity)
t is the time that we want to find.
Substitute in the equation to get the time as follows:
v = u + at
0 = 160 - 9.8t
9.8t = 160
t = 160/9.8 = 16.3265 sec
Therefore, the ball would take 16.3265 seconds before it starts falling back to the ground
Part (b):
First, we will get the total distance traveled by the ball as follows:
s = 0.5 (u+v)*t
s = 0.5(160+0)*16.3265
s = 1306.12 meters
The equation that we will use to solve this part is:
v^2 = u^2 + 2as where
v is the final velocity we want to calculate
u is the initial velocity of falling = 0 m/sec (ball starting falling when it reached the highest position, So, the final velocity in part a became the initial velocity here)
a is acceleration due to gravity = 9.8 m/sec^2 (positive as ball is moving downwards)
s is the distance covered = 1306.12 meters
Substitute in the above equation to get the final velocity as follows:
v^2 = u^2 + 2as
v^2 = (0)^2 + 2(9.8)(1306.12)
v^2 = 25599.952 m^2/sec^2
v = 159.99985 m/sec
Therefore, the velocity of the ball would be 159.99985 m/sec when it hits the ground.
