Complete Question
The cars of a roller-coaster ride have a speed of 19.0 km/h as they pass over the top of the circular track. Neglect any friction and calculate their speed v when they reach the horizontal bottom position. At the top position, the radius of the circular path of their mass centers is 21 m, and all six cars have the same mass.V = -18 m What is v?X km/h
Answer:

Explanation:
Velocity 
Radius 
initial velocity u
Generally the equation for Angle is mathematically given by




Generally
Height of mass



Generally the equation for Work Energy is mathematically given by

Therefore



Answer:
The value of Modulus of elasticity E = 85.33 ×

Beam deflection is = 0.15 in
Explanation:
Given data
width = 5 in
Length = 60 in
Mass of the person = 125 lb
Load = 125 × 32 = 4000
We know that moment of inertia is given as


I = 1.40625 
Deflection = 0.15 in
We know that deflection of the beam in this case is given as
Δ = 

E = 85.33 ×

This is the value of Modulus of elasticity.
Beam deflection is = 0.15 in
Answer:
4.5kg/min
Explanation:
Given parameters

if we take
The mass flow rate of the second stream = 
The mass flow rate of mixed exit stream = 
Now from mass conservation


The temperature of the mixed exit stream given as

Therefore the mass flow rate of second stream will be 4.5 kg/min.
Answer:

Explanation:
From the question we are told that:
Voltage 
Power 
Initial Power factor 
Final Power factor 
Generally the equation for Reactive Power is mathematically given by
Q=P(tan \theta_2-tan \theta_1)
Since




And




Therefore



Therefore
The size of the capacitor in vars that is necessary to raise the power factor to 0.9 lagging is

Answer:
a) Fb= 275.77 lb Fc= 142.75 lb
b) M = -779.97 lb.ft (i.e. 779.97 lb.ft in clockwise direction)
c) Fax = 195 lb
Fay = 337.75 lb
Fbx = 195 lb
Fby = 195 lb
Explanation:
Question: Three tugboats are used to turn a barge in a narrow channel. To avoid producing any net translation of the barge, the forces applied should be couples. The tugboat at point A applies a 390 lb force.
(a) Determine FB and FC so that only couples are applied.
(b) Using your answers to Part (a), determine the resultant couple moment that is produced.
(c) Resolve the forces at A and B into x and y components, and identify the pairs of forces that constitute couples.
Solution:
<u>For this problem Right hand side is positive X direction and Upwards is positive Y direction. Couples and moments will be considered positive in counterclockwise direction.</u>
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a) For no translation condition
∑
& ∑
Hence,


and

Inserting the value of
and solving the remaining equations simultaneously yields (magnitudes),
b) Summing up moments

(i.e. 779.97 lb.ft clockwise)
c)


