Answer:
Speed =0.283m/ s
Direction = 47.86°
Explanation:
Since it is a two dimensional momentum question with pucks having the same mass, we derive the momentum in xy plane
MU1 =MU2cos38 + MV2cos y ...x plane
0 = MU2sin38 - MV2sin y .....y plane
Where M= mass of puck, U1 = initial velocity of puck 1=0.46, U2 = final velocity of puck 1 =0.34, V2 = final velocity of puck 2, y= angular direction of puck2
Substitute into equation above
.46 = .34cos38 + V2cos y ...equ1
.34sin38 = V2sin y...equ2
.19=V2cos Y...x
.21=V2sin Y ...y
From x
V2 =0.19/cost
Sub V2 into y
0.21 = 0.19(Sin y/cos y)
1.1052 = tan y
y = 47.86°
Sub Y in to x plane equ
.19 = V2 cos 47.86°
V2=0.283m/s
Answer:
T = 1.12 10⁻⁷ s
Explanation:
This exercise must be solved in parts. Let's start looking for the electric field in the axis of the ring.
All the charge dq is at a distance r
dE = k dq / r²
Due to the symmetry of the ring, the field perpendicular to the axis is canceled, leaving only the field in the direction of the axis, if we use trigonometry
cos θ =
dEₓ = dE cos θ
cos θ = x / r
substituting
dEₓ = 
DEₓ = k dq x / r³
let's use the Pythagorean theorem to find the distance r
r² = x² + a²
where a is the radius of the ring
we substitute
dEₓ = 
we integrate
∫ dEₓ =k \frac{x}{(x^2 + a^2 ) ^{3/2} } ∫ dq
Eₓ = 
In the exercise indicate that the electron is very central to the center of the ring
x << a
Eₓ = 
if we expand in a series
we keep the first term if x<<a
Eₓ = 
the force is
F = q E
F = 
this is a restoring force proportional to the displacement so the movement is simple harmonic,
F = m a
the solution is of type
x = A cos (wt + Ф)
with angular velocity
w² = 
angular velocity and period are related
w = 2π/ T
we substitute
4π² / T² = \frac{keQ}{m a^3}
T = 2π 
let's calculate
T = 2π 
T = 2π pi 
T = 2π 17.9 10⁻⁹ s
T = 1.12 10⁻⁷ s
Answer:
a little less than 6 micrograms
Explanation:
The half-life of an element is defined as the time in which half of the isotope emits its radiation and becomes a different element. Therefore after 4.5 billion years the meteoroid will contain 12 micrograms of uranium, after 9 billion years will contain 6 micrograms. After 10 billion years will contain a little less than 6 micrograms.
Answer:
Work Done by the Brakes = - 60000 J
Negative sign indicates the opposite direction of force and displacement.
Explanation:
Assuming that frictional effects are negligible, we can say that all the work done by the brakes is used to stop the car. We can apply law of conservation of energy to this situation as follows:
Work Done by the Brakes = Change in Kinetic Energy
Work Done by the Brakes = Final Kinetic Energy - Initial Kinetic Energy
Final Kinetic Energy of the roller coaster will be 0. Because, the roller coaster will stop finally and its velocity will become zero.
Work Done by the Brakes = 0 J - 60000 J
<u>Work Done by the Brakes = - 60000 J</u>
<u>Negative sign indicates the opposite direction of force and displacement.</u>
The formula is:
v = v o + a t
6 = 10 + 3 * a
3 a = 10 - 6
a = 4 : 3
a = - 1.33 m/s² ( because the car slows down )
Answer: The average acceleration of the car is - 1.33 m/s²
