Answer:
v = ((m + M) / m)*√(2*g*h)
Explanation:
Given
m = mass of the projectile
M = mass of the ballistic pendulum
v = initial speed of the projectile
v' = speedof the system (pendulum + projectile) after the inelastic collision
h = maximum height reached for the system
Knowing that is an inelastic collision we have
m*v + M*(0) = (m+M)*v'
⇒ v' = m*v / (m+M)
After the collision, we apply the Principle of the Conservation of Energy
Ki + Ui = Kf + Uf
where
Ui = Kf = 0 J
then
Ki = Uf
0.5*(m+M)*v'² = (m+M)*g*h
⇒ 0.5*v'² = g*h
⇒ v'² = 2*g*h
⇒ (m*v / (m+M))² = 2*g*h
⇒ v = ((m+M) / m)*√(2*g*h)
Answer:
![\Delta x=245\ mm](https://tex.z-dn.net/?f=%5CDelta%20x%3D245%5C%20mm)
Explanation:
Given:
- mass of skier,
![m=70\ kg](https://tex.z-dn.net/?f=m%3D70%5C%20kg)
- initial velocity of skier,
![u=4\ m.s^{-1}](https://tex.z-dn.net/?f=u%3D4%5C%20m.s%5E%7B-1%7D)
- height of the hill,
![h=2\ m](https://tex.z-dn.net/?f=h%3D2%5C%20m)
- spring constant,
![k=2800\ N.m^{-1}](https://tex.z-dn.net/?f=k%3D2800%5C%20N.m%5E%7B-1%7D)
<u>final velocity of skier before coming in contact of spring:</u>
Using eq. of motion:
![v^2=u^2+gh](https://tex.z-dn.net/?f=v%5E2%3Du%5E2%2Bgh)
![v^2=4^2+9.8\times 2](https://tex.z-dn.net/?f=v%5E2%3D4%5E2%2B9.8%5Ctimes%202)
![v=5.9666\ m.s^{-1}](https://tex.z-dn.net/?f=v%3D5.9666%5C%20m.s%5E%7B-1%7D)
<u>Now the time taken by the skier to reach down:</u>
![v=u+gt](https://tex.z-dn.net/?f=v%3Du%2Bgt)
![5.9666=4+9.8\ t](https://tex.z-dn.net/?f=5.9666%3D4%2B9.8%5C%20t)
![t=0.2007\ s](https://tex.z-dn.net/?f=t%3D0.2007%5C%20s)
<u>Now we calculate force using Newton's second law:</u>
![F=\frac{dp}{dt}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7Bdp%7D%7Bdt%7D)
![F=\frac{m(v-u)}{t}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7Bm%28v-u%29%7D%7Bt%7D)
![F=\frac{70\times(5.9666-4)}{0.2007}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B70%5Ctimes%285.9666-4%29%7D%7B0.2007%7D)
![F\approx686\ N](https://tex.z-dn.net/?f=F%5Capprox686%5C%20N)
<u>∴Compression in spring before the skier momentarily comes to rest:</u>
![\Delta x=\frac{F}{k}](https://tex.z-dn.net/?f=%5CDelta%20x%3D%5Cfrac%7BF%7D%7Bk%7D)
![\Delta x=\frac{686}{2800}](https://tex.z-dn.net/?f=%5CDelta%20x%3D%5Cfrac%7B686%7D%7B2800%7D)
![\Delta x=0.245\ m](https://tex.z-dn.net/?f=%5CDelta%20x%3D0.245%5C%20m)
![\Delta x=245\ mm](https://tex.z-dn.net/?f=%5CDelta%20x%3D245%5C%20mm)
Can you post a picture of the whole thing please
<span>The number of protons determines what __________ a particular atom belongs to.
Answer = The number of protons </span><span>determines what element a particular atom belongs to.
So the correct and best answer choice is C. element.
Hope this helps.</span>
The vehicle speed required to drive on an icy road without sliding is 28.3 m/s.
The weight of the car is m = 1500 kg
The angle at which the road is inclined is θ = 10
The radius of curvature is r = 400m
The expression for the speed of the car required to travel on the road without sliding is V =![\sqrt{rgtan}](https://tex.z-dn.net/?f=%5Csqrt%7Brgtan%7D)
V =![\sqrt{400*9.8*tan10}](https://tex.z-dn.net/?f=%5Csqrt%7B400%2A9.8%2Atan10%7D)
V = 28.3 m/s
Velocity is the rate of change in direction of an object in motion measured by a specific time standard and observed from a specific reference point (for example, 60 km/h north). A key idea in kinematics, the branch of classical mechanics that studies the motion of bodies, is velocity.
The definition of velocity requires both its magnitude and its direction, since it is a physical vector quantity. Velocity is a coherently derived unit that is measured in the SI (metric system) as meters per second (m/s or m/s1). Velocity is a scalar absolute value (magnitude) of speed.
Learn more about Velocity here:
brainly.com/question/18084516
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