Answer:
Explanation:
Angular speed of hoop ω = v / r
= 8.90 / .27
= 32.96 rad / s
Translational kinetic energy = 1/2 mv²
= .5 x 1.8 x 8.9²
= 71.29 J
Rotational kinetic energy = 1/2 Iω²
= 1/2 mR²x ω²
= 1/2 mv²
= 71.29 J
Total kinetic energy
= 2 x 71.29
= 142.58 J
This energy will be used to attain height
If h be the height attained
mgh = 142.58
h = 142.58 / mg
= 142.58 / 1.8 x 9.8
= 8.08 m .
Answer:
v = √k/m x
Explanation:
We can solve this exercise using the energy conservation relationships
starting point. Fully compressed spring
Em₀ =
= ½ k x²
final point. Cart after leaving the spring
= K = ½ m v²
Em₀ = Em_{f}
½ k x² = ½ m v²
v = √k/m x
Answer:
The minimum speed = 
Explanation:
The minimum speed that the rocket must have for it to escape into space is called its escape velocity. If the speed is not attained, the gravitational pull of the planet would pull down the rocket back to its surface. Thus the launch would not be successful.
The minimum speed can be determined by;
Escape velocity = 
where: G is the universal gravitational constant, M is the mass of the planet X, and R is its radius.
If the appropriate values of the variables are substituted into the expression, the value of the minimum speed required can be determined.
Answer:
The slope of the line is zero
The object is at rest
Explanation:
The graph position vs time of an object represents the position of the object measured at different times.
The slope of this graph is given by:

where
is the increment in the y-variable
is the increment in the x-variable
However, we have that:
corresponds to
, the change in position of the object
corresponds to the change in time, 
Therefore, for a position-time graph the slope of the graph corresponds to the velocity of the object:

An object having a flat line on a position-time graph has a line with slope zero: therefore, its velocity is zero, and this means the object is at rest.