To solve the problem it is necessary to use Newton's second law and statistical equilibrium equations.
According to Newton's second law we have to

where,
m= mass
g = gravitational acceleration
For the balance to break, there must be a mass M located at the right end.
We will define the mass m as the mass of the body, located in an equidistant center of the corners equal to 4m.
In this way, applying the static equilibrium equations, we have to sum up torques at point B,

Regarding the forces we have,

Re-arrange to find M,



Therefore the maximum additional mass you could place on the right hand end of the plank and have the plank still be at rest is 16.67Kg
Answer:
a) The magnitude of the force is 968 N
b) For a constant speed of 30 m/s, the magnitude of the force is 1,037 N
Explanation:
<em>NOTE: The question b) will be changed in other to give a meaningful answer, because it is the same speed as the original (the gallons would be 1.9, as in the original).</em>
Information given:
d = 106 km = 106,000 m
v1 = 28 m/s
G = 1.9 gal
η = 0.3
Eff = 1.2 x 10^8 J/gal
a) We can express the energy used as the work done. This work has the following expression:

Then, we can derive the magnitude of the force as:

b) We will calculate the force for a speed of 30 m/s.
If the force is proportional to the speed, we have:

Answer:
13.33m/s
Explanation:
Given data
m1= 2000kg
u1= 20m/s
m2= 1500kg
u2= 0m/s
v1= 10m/s
Required
The speed of the sticks
We know that from the expression for the conservation of momentum
m1u1+m2u2= m1v1+m2v2
2000*20+1500*0=2000*10+1500*v2
40000=20000+1500v2
collect like terms
40000-20000= 1500v2
20000= 1500v2
v2= 20000/1500
v2= 13.33 m/s
Hence the velocity of the sticks is 13.33m/s
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