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Ksivusya [100]
3 years ago
12

A 4-lb ball b is traveling around in a circle of radius r1 = 3 ft with a speed (vb)1 = 6 ft>s. if the attached cord is pulled

down through the hole with a constant speed vr = 2 ft>s, determine the ball's speed at the instant r2 = 2 ft. how much work has to be done to pull down the cord? neglect friction and the size of the ball

Physics
1 answer:
Leya [2.2K]3 years ago
6 0
Position #1:
radius, r₁ = 3 ft
Tangential speed, v₁ = 6 ft/s

By definition, the angular speed is
ω₁ = v₁/r₁ = (3 ft/s) / (3 ft) = 1 rad/s

Position #2:
Radius, r₂ = 2 ft

By definition, the moment of inertia in positions 1 and 2 are respectively
I₁ = (4 lb)*(3 ft)² = 36 lb-ft²
I₂ = (4 lb)*(2 ft)² = 16 lb-ft²

Because momentum is conserved,
I₁ω₁ = I₂ω₂
Therefore the angular velocity in position 2 is
ω₂ = (I₁/I₂)ω₁
      = (36/16)*1 = 2.25 rad/s
The tangential velocity in position 2 is
v₂ = r₂ω₂ = (2 ft)*(225 rad/s) = 4.5 ft/s

At each position, there is an outward centripetal force.
In position 1, the centripetal force is
F₁ = m*(v²/r₂) = (4)*(6²/3) = 48 lbf
In position 2, the centripetal force is
F₂ = (4)*(4.5²/2) = 40.5 lbf

The radius diminishes at a rate of 2 ft/s.
Therefore the force versus distance curve is as shown below.

The work done is the area under the curve, and it is
W = (1/2)*(48.0+40.5 ft)*(3-2 ft) = 44.25 ft-lb

Answer:  44.25 ft-lb


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1.3 kg of water, at an initial temperature of 25oC, is heated at a rate of 100 W in a well-insulated container. How much time (i
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68.25 minutes.

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Power = Energy/time or

Power = Heat/time

P = Q/t....................... Equation 1

Q = Pt ........................ Equation 2

Where Q = quantity of heat, P = power, t = time.

Also,

Q = cm(t₂-t₁) ................. Equation 3

Where c = specific heat capacity of water, m = mass of water, t₁ = initial temperature of water, t₂ = final temperature of water.

substitute equation 2 into equation 3

Pt = cm(t₂-t₁) ............... Equation 4

make t the subject of the equation

t = cm(t₂-t₁)/P................ Equation 5

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Constant: 4200 J/kg.K

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