Answer:
A) the maximum acceleration the boulder can have and still get out of the quarry
B) how long does it take to be lifted out at maximum acceleration if it started from rest
Explanation:
A) 
let +y is upward. look below at the free body diagram. the mass M refers to the combined mass of the boulder and chain.
the weight of the chain is:    and maximum tension is
   and maximum tension is 
total mass and weight is : 


∑



B)
maximum acceleration

using 
to solve for t


 
        
             
        
        
        
Answer:
3.258 m/s
Explanation:
k = Spring constant = 263 N/m (Assumed, as it is not given)
x = Displacement of spring = 0.7 m (Assumed, as it is not given)
 = Coefficient of friction = 0.4
 = Coefficient of friction = 0.4
Energy stored in spring is given by

As the energy in the system is conserved we have

The speed of the 8 kg block just before collision is 3.258 m/s
 
        
             
        
        
        
Answer:
F = 0.00156[N]
Explanation:
We can solve this problem by using Newton's proposed universal gravitation law.

Where:
F = gravitational force between the moon and Ellen; units [Newtos] or [N]
G = universal gravitational constant = 6.67 * 10^-11 [N^2*m^2/(kg^2)]
m1= Ellen's mass [kg]
m2= Moon's mass [kg]
r = distance from the moon to the earth [meters] or [m].
Data:
G = 6.67 * 10^-11 [N^2*m^2/(kg^2)]
m1 = 47 [kg]
m2 = 7.35 * 10^22 [kg]
r = 3.84 * 10^8 [m]
![F=6.67*10^{-11} * \frac{47*7.35*10^{22} }{(3.84*10^8)^{2} }\\ F= 0.00156 [N]](https://tex.z-dn.net/?f=F%3D6.67%2A10%5E%7B-11%7D%20%2A%20%5Cfrac%7B47%2A7.35%2A10%5E%7B22%7D%20%7D%7B%283.84%2A10%5E8%29%5E%7B2%7D%20%7D%5C%5C%20F%3D%200.00156%20%5BN%5D)
This force is very small compare with the force exerted by the earth to Ellen's body. That is the reason that her body does not float away.
 
 
        
             
        
        
        
F = 52000 N
m = 1060 kg
a= F/m = 52000 N/1060 kg = 49.0566 m/s^2
 
        
             
        
        
        
Explanation:
First we will convert the given mass from lb to kg as follows.
         157 lb = 
                    = 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.
          
          = 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
       0.65% (w/w) = 
                            = 
                            = 
Therefore, calculate the volume which contains the amount of caffeine as follows.
    12818.7 mg = 12.8187 g = 
                        = 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.