a baseball bat balances 74.8 cm from one end. if an 0.542-kg glove is attached to that end, the balance point moves 25.9 cm toward the glove. calculate the mass of the bat
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The mass of the bat is approximately 1.56 kg. We can use the principle of moments to solve this problem. According to the principle of moments, the sum of the moments of all the forces acting on an object is equal to zero, assuming that the object is in equilibrium.
Let's assume that the bat has a mass of m kg and its center of mass is located at a distance of x cm from the end of the bat where the glove is attached. We can then write the following equation for the moments:
mx = (m+0.542)(x+74.8-25.9)
Here, the left-hand side represents the moment of the bat about the point where the glove is attached, and the right-hand side represents the moment of the bat and the glove about the same point. We have added the distance between the center of mass of the bat and the point where the glove is attached (74.8 cm) to the distance between the glove and the point where the glove is attached (-25.9 cm) to get the total distance between the center of mass of the combined system and the point where the glove is attached.
Simplifying the equation, we get:
m*x = (m+0.542)*48.9
Expanding the brackets, we get:
mx = 48.9m + 26.56
Rearranging and solving for m, we get:
m = 0.542*74.8/(-25.9) = 1.56 kg
Therefore, the mass of the bat is approximately 1.56 kg.
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I don't know what equation to use?
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Impulse = (force) x (length of time the force lasts)
I see where you doodled (60)(40) over on the side, and you'll be delighted
to know that you're on the right track !
Here's the mind-blower, which I'll bet you never thought of:
On a force-time graph, impulse (also change in momentum)
is just the area that's added under the graph during some time !
From zero to 60, the impulse is just the area of that right triangle
under the graph. The base of the triangle is 60 seconds. The
height of the triangle is 40N . The area of the triangle is not
the whole (base x height), but only 1/2 (base x height).
1/2 (base x height) = 1/2 (60s x 40N) = 1,200 newton-seconds
That's the impulse during the first 60 seconds. It's also the change in
the car's momentum during the first 60 seconds.
Momentum = (mass) x (speed)
If the car wasn't moving at all when the graph began, then its momentum is 1,200 newton-sec after 60 seconds. Through the convenience of the SI system of units, 1,200 newton-sec is exactly the same thing as 1,200 kg-m/s . The car's mass is 3 kg, so after 60 sec, you can write
Momentum = M x V = (3 kg) x (speed) = 1,200 kg-m/s
and the car's speed falls right out of that.
From 60to 120 sec, the change in momentum is the added area of that
extra right triangle on top ... it's 60sec wide and only 20N high. Calculate
its area, that's the additional impulse in the 2nd minute, which is also the
increase in momentum, and that'll give you the change in speed.
Answers
Answer:
655 nm
Explanation:
When the intereference is destructive then the thickness, d of antireflective film coating one side is given by
2d=w/2n
Where w is wavelength and n is the reflective index of the film
Making w the subject of formula then
w=4nd
Substituting 1.25 for n and 131 nm for d then the wavelength will be
w=4*1.25*131=655 nm
Therefore, the wavelength is equivalent to 655 nm
The formula for calculating the wavelength in an antireflective film involves thickness (d) and refractive index (n). For n = 1.25 and d = 131 nm, the resulting wavelength is 655 nm.
When light waves encounter a thin film, some of the waves are reflected from the top surface of the film, and some pass through it. These waves can interfere with each other, leading to constructive or destructive interference. In the case of antireflective coatings, destructive interference is desired to minimize reflection.
The formula you mentioned is used to calculate the thickness (d) of an antireflective film that results in destructive interference for a specific wavelength (w) of light. The formula is:
2d = w / (2n)
Where:
d is the thickness of the film.
w is the wavelength of light.
n is the refractive index of the film.
To find the wavelength (w) when given the thickness (d) and refractive index (n), you can rearrange the formula:
w = 4 * n * d
Now, let's calculate the wavelength using the provided values:
n = 1.25 (refractive index)
d = 131 nm (thickness in nanometers)
Substitute these values into the formula:
w = 4 * 1.25 * 131 = 655 nm
Therefore, the calculated wavelength (w) is 655 nanometers (nm). This means that for a film with a refractive index of 1.25 and a thickness of 131 nm, destructive interference occurs at a wavelength of 655 nm.
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The electromagnetic waves with an energy of are likely X-rays.
The energy of an electromagnetic wave is related to its frequency and wavelength by the equation:
E = hf = hc/λ
where:
E = energy of the electromagnetic wave
h = Planck's constant ()
f = frequency of the electromagnetic wave
c = speed of light ()
λ = wavelength of the electromagnetic wave
Solving for λ:
λ = hc/E =
λ ≈
This corresponds to a wavelength of about 44 nanometers, which falls in the range of X-rays. Therefore, the electromagnetic waves with an energy of are likely X-rays.
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Answers
Answer:
Magnitude of potential energy is increased by factor "2"
Explanation:
As we know that if two charge particles are placed at some distance "r" from each other then the electrostatic potential energy between two charge particles is given as
now we know that if the charge of one of the charge particle is increased to twice of initial charge then
now we can say from above two equations that
so on increase one of the charge to twice of initial value then the potential energy will become TWICE
Answers
Answer:
The motion graph provided represents the displacement of a toy train over time. The graph consists of two distinct segments: an initial period of constant velocity followed by a period of rest.
From the given information, we can determine that the train starts from a position of 2.0m north. This means that at t=0 (the beginning of the graph), the train is located 2.0m north of its starting point.
The first segment of the graph shows a straight line with a positive slope, indicating constant velocity. Since the train is moving north, the positive slope suggests that it is moving in the positive direction along the y-axis. The steeper the slope, the greater the velocity.
The second segment of the graph shows a horizontal line, indicating that the train is at rest. During this period, the train does not undergo any displacement and remains stationary.
To determine the total displacement of the train, we need to calculate the area under the graph. In this case, we have two separate areas to consider: one for each segment.
For the first segment, which represents motion, we can calculate the area by finding the area of a triangle. The formula for calculating the area of a triangle is A = 1/2 * base * height. In this case, the base corresponds to the time interval and the height corresponds to the displacement.
Let's assume that each unit on both axes represents 1 second and 1 meter, respectively. From the graph, we can estimate that the time interval for the first segment is approximately 4 seconds and that the displacement is approximately 8 meters (from t=0 to t=4). Therefore, using our formula, we can calculate:
A = 1/2 * 4s * 8m = 16m²
So, during this period of motion, the train has a displacement of 16 meters.
For the second segment, which represents rest, the train does not undergo any displacement. Therefore, the area under the graph is zero.
To calculate the total displacement of the train, we sum up the areas from both segments:
Total displacement = 16m² + 0m² = 16m²
Hence, the total displacement of the toy train is 16 meters.
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