How fast or slow an object is moving and in what direction
1 answer:
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Answer:
the block reaches higher than the sphere
\frac{y_{sphere}} {y_block} = 5/7
Explanation:
We are going to solve this interesting problem
A) in this case a sphere rolls on the ramp, let's find the speed of the center of mass at the exit of the ramp
Let's use the concept of conservation of energy
starting point. At the top of the ramp
Em₀ = U = m g y₁
final point. At the exit of the ramp
Em_f = K + U = ½ m v² + ½ I w² + m g y₂
notice that we include the translational and rotational energy, we assume that the height of the exit ramp is y₂
energy is conserved
Em₀ = Em_f
m g y₁ = ½ m v² + ½ I w² + m g y₂
angular and linear velocity are related
v = w r
the moment of inertia of a sphere is
I = m r²
we substitute
m g (y₁ - y₂) = ½ m v² + ½ ( m r²) (
)²
m g h = ½ m v² (1 + )
where h is the difference in height between the two sides of the ramp
h = y₂ -y₁
mg h = (
m v²)
v = √5/7 √2gh
This is the exit velocity of the vertical movement of the sphere
v_sphere = 0.845 √2gh
B) is the same case, but for a box without friction
starting point
Em₀ = U = mg y₁
final point
Em_f = K + U = ½ m v² + m g y₂
Em₀ = Em_f
mg y₁ = ½ m v² + m g y₂
m g (y₁ -y₂) = ½ m v²
v = √2gh
this is the speed of the box
v_box = √2gh
to know which body reaches higher in the air we can use the kinematic relations
v² = v₀² - 2 g y
at the highest point v = 0
y = vo₀²/ 2g
for the sphere
y_sphere = 5/7 2gh / 2g
y_esfera = 5/7 h
for the block
y_block = 2gh / 2g
y_block = h
therefore the block reaches higher than the sphere
Answer:
- After throwing the snow, velocity of the thrower is 2.33 m/s
- the velocity of the receiver is 0.026 m/s
Explanation:
Given the data in the question;
Using conservation of momentum,
Initial thrower has a momentum of mv; v
(69.5 kg + 0.0475 kg) × 2.35 m/s = 163.4366 kg.m/s
Now, When he throws it at 31.5 m/s, these constitutes a momentum of;
(0.0475 kg )(31.5 m/s) = 1.49625 kg.m/s
hence his momentum now is: 163.4366 - 1.49625 = 161.94035 kg.m/s
To get his velocity, we say;
161.94035 = mv
{ he lost weight of the snow ball so, m = 69.5 kg )
161.94035 = 69.5 × v
v = 161.94035 / 69.5
v = 2.33 m/s
Therefore, After throwing the snow, velocity of the thrower is 2.33 m/s
Next is the Receiver;
the receiver will gain momentum of 1.49625 kg.m/s
he has no momentum initially and after he catches the snow ball;
1.49625 kg.m/s = mv
1.49625 kg.m/s = ( 57.5 kg + 0.0475 kg ) × v
1.49625 kg.m/s = 57.5475 kg × v
v = ( 1.49625 kg.m/s ) / 57.5475 kg
v = 0.026 m/s
Therefore, the velocity of the receiver is 0.026 m/s
Using the formula v=f times lambada
then v=the speed of light.
and f=what’s we’re looking for
and lambada=the wavelength.
so then you sub what you have (v and lambada) in the formula.
then multiply the frequency(f) by the given wavelength and then solve for f
then v=the speed of light.
and f=what’s we’re looking for
and lambada=the wavelength.
so then you sub what you have (v and lambada) in the formula.
then multiply the frequency(f) by the given wavelength and then solve for f