To solve this problem we will apply the principle of conservation of energy, for which the initial potential and kinetic energy must be equal to the final one. The final kinetic energy will be transformed into rotational and translational energy, so the mathematical expression that approximates this deduction is
KE_i+PE_i = KE_{trans}+KE_{rot} +PE_f
, since initially cylinder was at rest
since at the ground potential energy is zero
The mathematical values are,
Here,
m = mass
g= Gravity
h = Height
V = Velocity
moment of Inertia in terms of its mass and radius
Angular velocity in terms of tangential velocity and its radius
Replacing the values we have that
mgh = \frac{1}{2} mv^2 +\frac{1}{2} (\frac{mr^2}{2})(\frac{v}{r})^2
gh = \frac{v^2}{2}+\frac{v^2}{4}
v = \sqrt{\frac{4gh}{3}}
From trigonometry the vertical height of inclined plane is the length of this plane for 
, then
Replacing,
Therefore the cylinder's speedat the bottom of the ramp is 3.32m/s
Answer:
V(t) = (q0/C) * e^(−t/RC
)
Explanation:
If there were a battery in the circuit with EMF E , the equation for V(t) would be V(t)=E−(RC)(dV(t)/dt) . This differential equation is no longer homogeneous in V(t) (homogeneous means that if you multiply any solution by a constant it is still a solution). However, it can be solved simply by the substitution Vb(t)=V(t)−E . The effect of this substitution is to eliminate the E term and yield an equation for Vb(t) that is identical to the equation you solved for V(t) . If a battery is added, the initial condition is usually that the capacitor has zero charge at time t=0 . The solution under these conditions will look like V(t)=E(1−e−t/(RC)) . This solution implies that the voltage across the capacitor is zero at time t=0 (since the capacitor was uncharged then) and rises asymptotically to E (with the result that current essentially stops flowing through the circuit).
The average speed of the runner is 8.7m/s.
Therefore, Option C) 8.7m/s is the correct answer.
Given the data in the question;
Distance covered; 
Time taken; 
Average speed; 
Speed is the rate at which an object covers a certain distance. It is expressed as:
Where s is speed, d is distance and t is time taken.
We substitute our given distance into the equation
The average speed of the runner is 8.7m/s
Therefore, Option C) 8.7m/s is the correct answer.
Learn more: brainly.com/question/21503615
Kinetic energy is the energy of an object that is moving. It is calculated from one-half the product of the mass and the change in square of the velocity of the object. It is the opposite of potential energy which the energy possessed by an object at rest. We calculate as follows:
KE = mΔv^2 / 2 = 45 ( 6^2 - 12^2 ) = -4860 J had been lost by the skater
Answer:
20 m
Explanation:
Given:
v = 0 m/s
a = -10 m/s²
t = 4 s / 2 = 2 s
Find: Δy
Δy = vt − ½ at²
Δy = (0 m/s) (2 s) − ½ (-10 m/s²) (2 s)²
Δy = 20 m
