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blagie
22 days ago
12

A test machine that kicks soccer balls has a 5-lb simulated foot attached to the end of a 6-ft long pendulum arm of negligible m

ass. Knowing that the arm is released from the horizontal position and that the coefficient of restitution between the foot and the 1-lb ball is 0.8, determine the exit velocity of the ball (a) if the ball is stationary, (b) if the ball is struck when it is rolling toward the foot with a velocity of 10 ft/s.
Engineering
1 answer:
choli [191]22 days ago
6 0

Answer:

a) v₂ = 26.6 ft/s

b) v₂ = 31.9 ft/s

Explanation:

a) Applying the principle of energy conservation for the soccer arm from the point of impact to its lowest point:

mgh=\frac{1}{2} mv^{2} \\v=\sqrt{2gh} =\sqrt{2*32.2*6} =19.66ft/s

The ball's velocity in the tangential direction is given by:

v₂*sinθ = v₁*sin30

With the values:

if v₁ = 0

θ = 0º

The restitution coefficient is:

e=\frac{v_{2}*cosO-v_{2}cos30 }{v*cos30-(-v_{1}*cos30 )} \\0.8=\frac{v_{2}cos0-v_{2}*cos30 }{19.66*cos30-(0*cos30)} \\v_{2} =\frac{v_{2}-13.6 }{cos30}

where O=θ

The aggregate momentum equation is:

mv-mv_{1} =mv_{2} +mv_{2} cos(O+30)\\, where O = θ

mv-mv_{1} =m(\frac{v_{2}-13.6 }{cos30} )+mv_{2} cos(O+30)

When we incorporate gravitational acceleration:

mgv-mgv_{1} =mg(\frac{v_{2}-13.6 }{cos30} )+mgv_{2} cos(O+30)\\5*19.66-1*0=5*(\frac{v_{2}-13.6 }{cos30} )+1*v_{2} cos(O+30)

Isolating v₂ results in:

v₂ = 26.6 ft/s

b) To find the ball's velocity, we utilize:

v₂ * sinθ = v₁ * sin30

if v₁ = 10 ft/s

then v₂ * sinθ = 10 * sin30

thus sinθ = 5/v₂

The restitution coefficient remains:

e=\frac{v_{2}*cosO-v_{2}cos30 }{v*cos30-(-v_{2}*cos30) } \\0.8=\frac{v_{2}cosO-v_{2}cos30 }{19.66*cos30-(-10*cos30)} \\v_{2} =\frac{v_{2}cos30-20.55}{cos30}

where O = θ

mgv-mgv_{1} =mgv_{2} +mgv_{2} cos(O+30)\\5*19.66-1*0=5v_{2} +v_{2} cos(O+30)\\98.3=5v_{2}+v_{2} cosOcos30-v_{2} sinOsin30

Solving for v₂ yields:

v₂ = 31.9 ft/s

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Answer:

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A) This statement shows the number 34.789 in a field that provides eight character spaces with two decimal precision. cout<<setw(9)<<fixed<<setprecision(2)<<34.789;

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23 days ago
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Based on the first equation

V_2 = \frac{p_1 V_1 T_2}{T_1 p_2}, we find

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5 days ago
You want to know your grade in Computer Science, so write a program that continuously takes grades between 0 and 100 to standard
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Below is the code provided in Python.

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The force of magnitude F acts along the edge of the triangular plate. Determine the moment of F about point O. Find the general
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Answer:

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Calculate the moment M_o at the origin and its direction:

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Response:

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Clarification:

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