Answer:
v = 4.4271 m/s
Explanation:
Given
m = 3 Kg
R = 0.2 m
∅ = 15°
h = 1.5 m
g = 9.8 m/s²
v = ?
Ignoring frictional losses, at the bottom of the plane
Total kinetic energy is = Potential Energy at the top of plane
Using Law of conservation of energy we have
U = Kt + Kr
m*g*h = 0.5*m*v² + 0.5*I*ω²
knowing that
Icylinder = 0.5*m*R²
ω = v/R
we have
m*g*h = 0.5*m*v² + 0.5*(0.5*mR²)*(v/R)² = 0.75*m*v²
⇒ v = √(g*h/0.75) = √(9.8 m/s²*1.5 m/0.75)
⇒ v = 4.4271 m/s
Answer:
doubled
Explanation:
F=ma1----------(1)
2F = ma2-------(2)
Divide 2nd equation by 1st one
we get a1×2=a2
The average velocity is -4.17 m/s
Explanation:
The average velocity of a body is given by:

where
d is the displacement of the body
t is the time elapsed
For the student in this problem, we have:
Initial position: 
Final position: 
So the displacement is

The time elapsed is
t = 60 s
Therefore, the average velocity is

Where the negative sign means the student is moving towards the origin.
Learn more about average speed and velocity:
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Answer:
When there is a change in magnetic flux linkage through a loop of wire, an electromotive force is induced in the loop, according to the Faraday-Newmann-Lenz Law:

where
N is the number of turns in the loop
is the change in magnetic flux through the loop
is the time elapsed
The negative sign in the formula represents Lenz's Law, and tells us about the direction of the electromotive force.
In fact, the negative sign means that the direction of the induced emf is such that to oppose to the change in the magnetic flux that originated the induced emf.
This is a consequence of the law of conservation of energy: no energy can be created out of nowhere. In fact, when the emf is induced in the loop, electrical energy appears in the circuit; however, this electric energy cannot come out of nowhere. Instead, it is just "created" from the transformation of some other form of energy (for instance, the mechanical energy that is used to move the loop in the magnetic field, and changing its magnetic flux).
The negative sign in Lenz's Law tells exactly this: the direction of the induced emf is such that it opposes the initial change in magnetic flux that generated the induced emf, so that overall the total energy is conserved.
solution:
We know v0 = 0, a = 9.8, t = 4.0. We need to solve for v
so,
we use the equation:
v = v0 + at
v = 0 + 9.8*4.0
v = 39.2 m/s
Now we just need to solve for d, so we use the equation:
d = v0t + 1/2*a*t^2
d = 0*4.0 + 1/2*9.8*4.0^2
d = 78.4 m