Answer:
v_{f} = 74 m/s, F = 230 N
Explanation:
We can work on this exercise using the relationship between momentum and moment
I = ∫ F dt = Δp
bold indicates vectors
we can write this equations in its components
X axis
Fₓ t = m ( -v_{xo})
Y axis
t = m (v_{yf} - v_{yo})
in this case with the ball it travels horizontally v_{yo} = 0
Let's use trigonometry to write the final velocities and the force
sin 30 = v_{yf} / vf
cos 30 = v_{xf} / vf
v_{yf} = vf sin 30
v_{xf} = vf cos 30
sin40 = F_{y} / F
F_{y} = F sin 40
cos 40 = Fₓ / F
Fₓ = F cos 40
let's substitute
F cos 40 t = m ( cos 30 - vₓ₀)
F sin 40 t = m (v_{f} sin 30-0)
we have two equations and two unknowns, so the system can be solved
F cos 40 0.1 = 0.4 (v_{f} cos 30 - 20)
F sin 40 0.1 = 0.4 v_{f} sin 30
we clear fen the second equation and subtitles in the first
F = 4 sin30 /sin40 v_{f}
F = 3.111 v_{f}
(3,111 v_{f}) cos 40 = 4 v_{f} cos 30 - 80
v_{f} (3,111 cos 40 -4 cos30) = - 80
v_{f} (- 1.0812) = - 80
v_{f} = 73.99
v_{f} = 74 m/s
now we can calculate the force
F = 3.111 73.99
F = 230 N
Answer:
0 degrees
Explanation:
Let 
are two forces. The resultant of two forces acting on the same point is given by :
Where 
is the angle between two forces
When 
i.e. when two forces are parallel to each other,
When 
i.e. when two forces are parallel to each other,
When 
i.e. when two forces are parallel to each other,
It is clear that the resultant of two forces acting on the same point simultaneously will be the greatest when the angle between them is 0 degrees. Hence, this is the required solution.
Answer:
x = 0.54 m
y = 0.058 m
Explanation:
m = mass of the bullet = 16 g = 0.016 kg
v = speed of bullet before collision = 240 m/s
M = mass of the pendulum = 3.6 kg
L = length of the string = 2.5 m
h = height gained by the pendulum after collision
V = speed of the bullet and pendulum combination
Using conservation of momentum
m v = (m + M) V
(0.016) (240) = (0.016 + 3.6) V
V = 1.062 m/s
Using conservation of energy
Potential energy gained by bullet and pendulum combination = Kinetic energy of bullet and pendulum combination
(m + M) g h = (0.5) (m + M) V²
(9.8) h = (0.5) (1.062)²
h = 0.058 m
y = vertical displacement = h = 0.058 m
x = horizontal displacement
horizontal displacement is given as
x = sqrt(L² - (L - h)²)
x = sqrt(2.5² - (2.5 - 0.058)²)
x = 0.54 m
