Answer:
(a) -472.305 J
(b) 1 m
Explanation:
(a)
Change in mechanical energy equals change in kinetic energy
Kinetic energy is given by
Initial kinetic energy is 
Since he finally comes to rest, final kinetic energy is zero because the final velocity is zero
Change in kinetic energy is given by final kinetic energy- initial kinetic energy hence
0-472.305 J=-472.305 J
(b)
From fundamental kinematic equation
Where v and u are final and initial velocities respectively, a is acceleration, s is distance
Making s the subject we obtain
but a=\mu g hence
Answer:
Approximately 
(assuming that the acceleration due to gravity is 
.)
Explanation:
Let 
denote the first piston's contact area with the fluid. Let 
denote the second piston's contact area with the fluid.
Similarly, let 
and 
denote the size of the force on the two pistons. Since the person is placing all her weight on the first piston:
.
Since both pistons fit into cylinders, the two contact surfaces must be circles. Keep in mind that the area of a square is equal to 
times its radius, squared:
.
.
By Pascal's Law, the pressure on the two pistons should be the same. Pressure is the size of normal force per unit area:
.
For the pressures on the two pistons to match:
.
, , and have all been found. The question is asking for . Rearrange this equation to obtain:
.
Evaluate this expression to obtain the value of , which represents the force on the piston with the larger diameter:
.
The type of star is the north star
Answer:
The magnitude and direction of the force applied by Steinberg are approximately 15.192 newtons and 126.704º.
Explanation:
The chew toy is at equilibrium and experimenting three forces from three distinct dogs. The Free Body Diagram depicting the system is attached below. By Newton's Laws we construct the following equations of equilibrium: (<em>Sp</em> is for Spot, <em>F</em> is for Fido and <em>St</em> is for Steinberg) All forces and angles are measured in newtons and sexagesimal degrees, respectively:
(1)
(2)
If we know that 
, 
and 
, then the components of the force done by Steinberg on the chewing toy is:
The magnitud of the force is determined by Pythagorean Theorem:
Since the direction of this force is in the 3rd Quadrant on Cartesian plane, we determine the direction of the force with respect to the eastern semiaxis:
The magnitude and direction of the force applied by Steinberg are approximately 15.192 newtons and 126.704º.
Answer:
The increase in gravitational potential energy is the same in both cases
Explanation:
It is easier to climb a mountain in a zigzag way rather than climbing on a straight line but since the distance is the same ( vertical height ) , mass and gravity is the same. Hence the increase in gravitational potential energy is the same in both cases.
gravitational potential energy = mgh ( same in both cases )
m = mass
g = acceleration due to gravity
h = distance ( vertical height )
