Answer:
a) L=0. b) L = 262 k ^ Kg m²/s and c) L = 1020.7 k^ kg m²/s
Explanation:
It is angular momentum given by
L = r x p
Bold are vectors; where L is the angular momentum, r the position of the particle and p its linear momentum
One of the easiest ways to make this vector product is with the use of determinants
![{array}\right] \left[\begin{array}{ccc}i&j&k\\x&y&z\\px&py&pz\end{array}\right]](https://tex.z-dn.net/?f=%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5Cx%26y%26z%5C%5Cpx%26py%26pz%5Cend%7Barray%7D%5Cright%5D)
Let's apply this relationship to our case
Let's start by breaking down the speed
v₀ₓ = v₀ cosn 45
voy =v₀ sin 45
v₀ₓ = 9 cos 45
voy = 9 without 45
v₀ₓ = 6.36 m / s
voy = 6.36 m / s
a) at launch point r = 0 whereby L = 0
. b) let's find the position for maximum height, we can use kinematics, at this point the vertical speed is zero
vfy² = voy²- 2 g y
y = voy² / 2g
y = (6.36)²/2 9.8
y = 2.06 m
Let's calculate the angular momentum
L= ![\left[\begin{array}{ccc}i&j&k\\x&y&0\\px&0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5Cx%26y%260%5C%5Cpx%260%260%5Cend%7Barray%7D%5Cright%5D)
L = -px y k ^
L = - (m vox) (2.06) k ^
L = - 20 6.36 2.06 k ^
L = 262 k ^ Kg m² / s
The angular momentum is on the z axis
c) At the point of impact, at this point the height is zero and the position on the x-axis is the range
R = vo² sin 2θ / g
R = 9² sin (2 45) /9.8
R = 8.26 m
L =
L = - x py k ^
L = - x m voy
L = - 8.26 20 6.36 k ^
L = 1020.7 k^ kg m² /s
Answer:
4.22 m
Explanation:
Una rampa es una máquina que se utiliza para levantar un objeto con una fuerza menor a la que realmente necesitarías. Cuanto mayor sea la longitud de la rampa, menor será la magnitud de la fuerza necesaria para levantar el objeto.
Dado que:
altura de la rampa = 1.5 m, carga = 4900 N, fuerza aplicada = 1633.33 N.
La fórmula de la rampa se da como:
fuerza aplicada * longitud de la rampa = peso de la carga * altura de la rampa
1633.33 * longitud de la rampa = 4900 * 1.5
longitud de la rampa = 4900 * 1.5 / 1633.33
longitud de la rampa = 4.22 m
Answer:
Explanation:
Potential energy, which is the energy a body assumes at a position, can be calculated using the formula:
P.E = m × g × h
Where;
m = mass (kg)
g = acceleration due to gravity (10m/s²)
h = height (m)
Answer:
Power= 6.84×10⁸ W
Explanation:
Given Data
Niagara falls at rate of=1.4×10⁶ kg/s
falls=49.8 m
To find
Power Generated
Solution
Regarding this problem
GPE (gravitational potential energy) declines each second is given from that you will find much the kinetic energy of the falling water is increasing each second.
So power can be found by follow
Power= dE/dt = d/dt (mgh)
Power= gh dm/dt
Power= 1.4×10⁶ kg/s × 9.81 m/s² × 49.8 m
Power= 6.84×10⁸ W