Explanation:
(a) Draw a free body diagram of the cylinder at the top of the loop. At the minimum speed, the normal force is 0, so the only force is weight pulling down.
Sum of forces in the centripetal direction:
∑F = ma
mg = mv²/RL
v = √(g RL)
(b) Energy is conserved.
EE = KE + RE + PE
½ kd² = ½ mv² + ½ Iω² + mgh
kd² = mv² + Iω² + 2mgh
kd² = mv² + (m RC²) ω² + 2mg (2 RL)
kd² = mv² + m RC²ω² + 4mg RL
kd² = mv² + mv² + 4mg RL
kd² = 2mv² + 4mg RL
kd² = 2m (v² + 2g RL)
d² = 2m (v² + 2g RL) / k
d = √[2m (v² + 2g RL) / k]
25% i believe because if were talking 50 percent half it would be 25.
Answer:
Δy = 6.05 mm
Explanation:
The double slit phenomenon is described by the expression
d sin θ = m λ constructive interference
d sin θ = (m + ½) λ destructive interference
m = 0,±1, ±2, ...
As they tell us that they measure the dark stripes, we are in a case of destructive interference, let's use trigonometry to find the sins tea
tan θ = y / x
y = x tan θ
In the interference experiments the measured angle is very small so we can approximate the tangent
tan θ = sin θ / cos θ
cos θ = 1
tan θ = sin θ
y = x sin θ
We substitute in the destructive interference equation
d (y / x) = (m + ½) λ
y = (m + ½) λ x / d
The first dark strip occurs for m = 0 and the third dark strip for m = 2. Let's find the distance for these and subtract it
m = 0
y₀ = (0+ ½) 480 10⁻⁹ 1.7 / 0.27 10⁻³
y₀ = 1.511 10⁻³ m
m = 2
y₂ = (2 + ½) 480 10⁻⁹ 1.7 / 0.27 10⁻³
y₂ = 7.556 10⁻³ m
The separation between these strips is Δy
Δy = y₂-y₀
Δy = (7.556 - 1.511) 10⁻³
Δy = 6.045 10⁻³ m
Δy = 6.05 mm
Answer:
Explanation:
Given that
Radius of track = R
Radius of ball = r
The ball can be treated as solid sphere, so
The moment of inertia of ball
When the ball reach at the lowest position then it will have both angular and linear speed.
Condition for rolling without slipping v= ωr
Form energy conservation
v= ωr
