Answer:
vector quantities are resolved into their component form (along the x and y-axis) before adding them. Let us assume that two vectors are
→
a
=
x
1
^
i
+
y
1
^
j
and
→
b
=
x
2
^
i
+
y
2
^
j
, we can find the sum of two vectors as follows.
→
a
+
→
b
=
x
1
^
i
+
y
1
^
j
+
x
2
^
i
+
y
2
^
j
=
(
x
1
+
x
2
)
^
i
+
(
y
1
+
y
2
)
^
j
The direction of the sum of the vectors (with positive x-axis) is,
θ
=
tan
−
1
(
y
1
+
y
2
x
1
+
x
2
)
i think its d im not sure
Answer:
1.84 m
Explanation:
For the small lead ball to be balanced at the tip of the vertical circle just before it is released, the reaction force , N equal the weight of the lead ball W + the centripetal force, F. This normal reaction ,N also equals the tension T in the string.
So, T = mg + mrω² = ma where m = mass of small lead ball, g = acceleration due to gravity = 9.8 m/s², r = length of rope = 1.10 m and ω = angular speed of lead ball = 3 rev/s = 3 × 2π rad/s = 6π rad/s = 18.85 rad/s and a = acceleration of normal force. So,
a = g + rω²
= 9.8 m/s² + 1.10 m × (18.85 rad/s)²
= 9.8 m/s² + 390.85 m/s²
= 400.65 m/s²
Now, using v² = u² + 2a(h₂ - h₁) where u = initial velocity of ball = rω = 1.10 m × 18.85 rad/s = 20.74 m/s, v = final velocity of ball at maximum height = 0 m/s (since the ball is stationary at maximum height), a = acceleration of small lead ball = -400.65 m/s² (negative since it is in the downward direction of the tension), h₁ = initial position of lead ball above the ground = 1.3 m and h₂ = final position of lead ball above the ground = unknown.
v² = u² + 2a(h₂ - h₁)
So, v² - u² = 2a(h₂ - h₁)
h₂ - h₁ = (v² - u²)/2a
h₂ = h₁ + (v² - u²)/2a
substituting the values of the variables into the equation, we have
h₂ = 1.3 m + ((0 m/s)² - (20.74 m/s)²)/2(-400.65 m/s²)
h₂ = 1.3 m + [-430.15 (m/s)²]/-801.3 m/s²
h₂ = 1.3 m + 0.54 m
h₂ = 1.84 m
Answer:
(a) 32.5 kgm/s
(b) 32.5 Ns
(c) 10.8 N
Explanation:
The change in momentum can be calculated from the definition of linear momentum:
Then, the change in momentum of the body is of 32.5 kgm/s (a).
Now, from the impulse-momentum theorem, we know that the change in momentum of a body 
is equal to the impulse 
exerted to it. So, the impulse produced by the force equals 32.5 kgm/s (or 32.5 Ns) (b).
Finally, since we know the value of the impulse and the interval of time, we can easily solve for the magnitude of the force:
It means that the magnitude of the force is of 10.8N (c).
Answer:
where is the box? ehh bring the box out
