Answer and Explanation: Kinetic energy is related to movement: it is the energy an object possesses during the movement. it is calculated as:
For the object thrown in the air:
![K=\frac{1}{2}.2.[v(t)]^{2}](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7D.2.%5Bv%28t%29%5D%5E%7B2%7D)
Kinetic energy of the object as a function of time:
Potential energy is the energy an object possesses due to its position in relation to other objects. It is calculated as:
For the object thrown in the air:
Potential energy as function of time:
Total kinetic and potential energy, also known as mechanical energy is
TME = 
+ (
)
TME = 1752
The expression shows that total energy of an object thrown in the air is constant and independent of time.
Answer:
6.18 m/s
Explanation:
Roller skate collision
The final direction of the system (me=M + person=P) velocity vector is at an angle; Ф, to the direction running south to north. Apply the component form of the impulse-momentum equation, firstly;
x-axis component form (+x east);
+ 
+ 
= 
+
Ф
60 ·8 + 0 = (60 + 80)
Ф
480 = 140
Ф................. (I)
y-axis component form (+y north);
+ 
+ 
= 
+ 
Ф
0 + 80.9 = (60 + 80)
Ф
720=
140Ф
140Vf=
Ф......................................(2)
Substituting (2) into (1) to give the angle;
480 = 720tan Ф
Ф = arctan(0.67) =33.69°.......................(3)
Evaluating (1) with (3) gives the velocity magnitude
480 = 140Vfsin 33.69°
Vf=6.18 m/s
note 1:
This angle corresponds to a direction; 90° - 33.69° = 56.31° north of east.
Answer:
V
I and II
III and IV
Explanation:
The impulse is equal to the change in momentum of the object involved, so we can calculate the change in momentum in each situation and compare them all.
Taking always east as positive direction, and labelling
u the initial velocity
v the final velocity
m = 1000 kg the mass (which is always equal)
We find:
(i)
u = 25 m/s
v = 0
(II)
u = 25 m/s
v = 0
(III)
In this case,
F = 2000 N is the force
is the time
So the magnitude of the impulse is
(IV)
F = 2000 N is the force
is the time
So the magnitude of the impulse is
(V)
u = 25 m/s
v = -25 m/s
So the ranking from largest to smallest is:
V
I and II
III and IV
when the apple moves in a horizontal circle, the tension force in the string provides the necessary centripetal force to move in circle. the tension in the string is given as
T=mv²/r
where T = tension force in the string , m = mass of the apple
v = speed of apple , r = radius of circle.
clearly , tension force depends on the square of the speed. hence greater the speed, greater will be the tension force.
at some point , the speed becomes large enough that it makes the tension force in the string becomes greater than the tensile strength of the string. at that point , the string breaks
Answer:
T=1022.42 N
Explanation:
Given that
l = 32 cm ,μ = 1.5 g/cm
L =2 m ,V= 344 m/s
The pipe is closed so n= 3 ,for first over tone
f= 129 Hz
The tension in the string given as
T = f²(4l²) μ
Now by putting the values
T = f²(4l²) μ
T = 129² x (4 x 0.32²) x 1.5 x 10⁻³ x 100
T=1022.42 N
