A bee loaded with pollen flies in a circular path at a constant speed of 3.20 m/s. If the mass of the bee is 133 mg and the radi
2 answers:
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Each ion contains three extra protons. Hence, the extra charge on each
=
C
Total charge = 0.035 pC
Total charge (Q) = C
Let the number of ions be n.
According to question:
n = 72917
Hence, the total number of ions needed to be transferred is 72917
The momentum of the red cart before the collision is 0.2 kgm/s and the blue cart is 0.
The momentum of the red cart after the collision is 0.05 kgm/s and the blue cart is 0.15 kgm/s.
The change in momentum of the system of the carts is 0.
<h3>Initial momentum of the carts before collision</h3>The momentum of the carts before the collision is calculated as follows;
P(red) = 0.5 kg x 0.4 m/s = 0.2 kgm/s
P(blue) = 1.5 x 0 = 0
<h3>Momentum of the carts after collision</h3>The momentum of the carts after the collision is calculated as follows;
P(red) = 0.5 x 0.1 = 0.05 kgm/s
P(blue) = 1.5 0.1 = 0.15 kgm/s
<h3>Change in momentum of the carts</h3>ΔP = (0.05 + 0.15) - (0.2)
ΔP = 0
Learn more about momentum here: brainly.com/question/7538238
Explanation:
<em>(a) On the dots below, which represent the sphere, draw and label the forces (not components) that are exerted on the sphere at point A and at point B, respectively. Each force must be represented by a distinct arrow starting on and pointing away from the dot.</em>
At point A, there are three forces acting on the sphere: weight force mg pulling down, normal force N pushing left, and static friction force Fs pushing down.
At point B, there are three forces acting on the sphere: weight force mg pulling down, normal force N pushing down, and static friction force Fs pushing right.
<em>(b) i. Derive an expression for the speed of the sphere at point A.</em>
Energy is conserved:
PE = PE + KE + RE
mgH = mgR + ½mv² + ½Iω²
mgH = mgR + ½mv² + ½(⅖mr²)(v/r)²
mgH = mgR + ½mv² + ⅕mv²
gH = gR + ⁷/₁₀ v²
v² = 10g(H−R)/7
v = √(10g(H−R)/7)
<em>ii. Derive an expression for the normal force the track exerts on the sphere at point A.</em>
Sum of forces in the radial (-x) direction:
∑F = ma
N = mv²/R
N = m (10g(H−R)/7) / R
N = 10mg(H−R)/(7R)
<em>(c) Calculate the ratio of the rotational kinetic energy to the translational kinetic energy of the sphere at point A.</em>
RE / KE
= (½Iω²) / (½mv²)
= ½(⅖mr²)(v/r)² / (½mv²)
= (⅕mv²) / (½mv²)
= ⅕ / ½
= ⅖
<em>(d) The minimum release height necessary for the sphere to travel around the loop and not lose contact with the loop at point B is Hmin. The sphere is replaced with a hoop of the same mass and radius. Will the value of Hmin increase, decrease, or stay the same? Justify your answer.</em>
When the sphere or hoop just begins to lose contact with the loop at point B, the normal force is 0. Sum of forces in the radial (-y) direction:
∑F = ma
mg = mv²/R
gR = v²
Applying conservation of energy:
PE = PE + KE + RE
mgH = mg(2R) + ½mv² + ½Iω²
mgH = 2mgR + ½mv² + ½(kmr²)(v/r)²
mgH = 2mgR + ½mv² + ½kmv²
gH = 2gR + ½v² + ½kv²
gH = 2gR + ½v² (1 + k)
Substituting for v²:
gH = 2gR + ½(gR) (1 + k)
H = 2R + ½R (1 + k)
H = ½R (4 + 1 + k)
H = ½R (5 + k)
For a sphere, k = 2/5. For a hoop, k = 1. As k increases, H increases.
<em>(e) The sphere is again released from a known height H and eventually leaves the track at point C, which is a height R above the bottom of the loop, as shown in the figure above. The track makes an angle of θ above the horizontal at point C. Express your answer in part (e) in terms of m, r, H, R, θ, and physical constants, as appropriate. Calculate the maximum height above the bottom of the loop that the sphere will reach.</em>
C is at the same height as A, so we can use our answer from part (b) to write an equation for the initial velocity at C.
v₀ = √(10g(H−R)/7)
The vertical component of this initial velocity is v₀ sin θ. At the maximum height, the vertical velocity is 0. During this time, the sphere is in free fall. The maximum height reached is therefore:
v² = v₀² + 2aΔx
0² = (√(10g(H−R)/7) sin θ)² + 2(-g)(h − R)
0 = 10g(H−R)/7 sin²θ − 2g(h − R)
2g(h − R) = 10g(H−R)/7 sin²θ
h − R = 5(H−R)/7 sin²θ
h = R + ⁵/₇(H−R)sin²θ
