Answer:
vf = 3.27[m/s]
Explanation:
In order to solve this problem we must analyze each body individually and find the respective equations. The free body diagram of each body (box and bucket) should be made, in the attached image we can see the free body diagrams and the respective equations.
With the first free body diagram, we determine that the tension T should be equal to the product of the mass of the box by the acceleration of this.
With the second free body diagram we determine another equation that relates the tension to the acceleration of the bucket and the mass of the bucket.
Then we equalize the two stress equations and we can clear the acceleration.
a = 3.58 [m/s^2]
As we know that the bucket descends 1.5 [m], this same distance is traveled by the box, as they are connected by the same rope.
![x = \frac{1}{2} *a*t^{2}\\1.5 = \frac{1}{2}*(3.58) *t^{2} \\t = 0.91 [s]](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2Aa%2At%5E%7B2%7D%5C%5C1.5%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%283.58%29%20%2At%5E%7B2%7D%20%5C%5Ct%20%3D%200.91%20%5Bs%5D)
And the speed can be calculated as follows:
![v_{f}=v_{o}+a*t\\v_{f}=0+(3.58*0.915)\\v_{f}= 3.27[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D%2Ba%2At%5C%5Cv_%7Bf%7D%3D0%2B%283.58%2A0.915%29%5C%5Cv_%7Bf%7D%3D%203.27%5Bm%2Fs%5D)
Answer:
1. 218.55 N
2. 
3. 
Explanation:
Part 1;
Net force
where m is mass, g is gravitational force and
is the angle of inclination

Frictional force,
is given by
where
is the coefficient of static friction


Since
, therefore, the block doesn’t slip and the frictional force acting is mgh=218.55N
Part 2.
Using the relationship that
Frictional force 



The maximum angle of inclination 

Part 3:
Net force on the object is given by
where
is the coefficient of kinetic friction

= 9.8 ( sin 38 - (0.51) cos 38 )
= 
K.E.= 1/2 x MV^2 = 1/2 x 40(kg) x (25x25) =12500J
Answer:
0.915 rad or 52.44 degrees
Explanation:
Let g = 10 m/s2. We can calculate the gravity force acting on center of mass of the new 8.75 kg pole:

The moment is the dot product of force and moment arm

where θ is the angle between the gravity force and the pole, or between the pole and the wall. As M can be at its max, which is 40 Nm, we can solve for θ:


