A displacement vector is 34.0 m in length and is directed 60.0° east of north. What are the components of this vector? Northward
1 answer:
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Answer:
(moving toward the incline.)
(moving away from the incline.)
(Assumption: .)
Explanation:
If , the potential energy of the block of
would be
when it was at the top of the incline.
If friction is negligible, all these energies would be converted to kinetic energy when this block reaches the bottom of the incline. There shouldn't be any energy loss along the horizontal surface, either. Therefore, the kinetic energy of this block right before the collision would also be approximately
.
Calculate the velocity of that based on its kinetic energy:
.
A collision is considered as an elastic collision if both momentum and kinetic energy are conserved.
Initial momentum of the two blocks:
.
.
Sum of the momentum of each block right before the collision: approximately .
Sum of the momentum of each block right after the collision: .
For momentum to conserve in this collision, and
should ensure that
.
Kinetic energy of the two blocks right before the collision: approximately and
. Sum of these two values: approximately
.
Sum of the energy of each block right after the collision:
.
Similarly, for kinetic energy to conserve in this collision, and
should ensure that
.
Combine to obtain two equations about and
(given that
whereas
.)
.
Solve for and
(ignore the root where
.)
.
The collision flipped the sign of the velocity of the block. In other words, this block is moving backwards towards the incline after the collision.
Answer:
The new potential energy decreases by the factor of 2 to the old potential energy.
Explanation:
Capacitance of a parallel plate capacitor is given by the relation :
C = (ε₀A)/d
Here ε₀ is vacuum permittivity, A is area of the capacitor plate and d is the distance between them.
Potential energy of the capacitor, U =
Here V is the potential difference between the plates.
According to the problem, the distance between the plates get double but area remains same. So,
d₁ = 2d
Here d₁ is new distance between the plates.
Hence, new capacitance is :
C₁ = (ε₀A)/d₁ = (ε₀A)/2d = C/2
The capacitor have same potential difference that is V. Hence, the new potential energy is :
U₁ = =
U₁ = U/2