The variables that show a direct relationship are :
- The speed of a car and the distance traveled
- Number of students in a cafeteria and the amount of food consumed
- The distance a planet is from the sun and that planet's temperature
- The mass of a space shuttle and its acceleration through space
In direct relationship, when one factor is increased/decreased , it will directly cause the other factor to be increased/decreased
Vx=cos60(4)
x-component of velocity
<span>If you think about it, it makes a right triangle when you combine all the different types of forces together such as v, vx and vy. Then, you can use trigonometry and soh cah toa in order to figure out vx. </span>
It has three significant figure
Ok, assuming "mj" in the question is Megajoules MJ) you need a total amount of rotational kinetic energy in the fly wheel at the beginning of the trip that equals
(2.4e6 J/km)x(300 km)=7.2e8 J
The expression for rotational kinetic energy is
E = (1/2)Iω²
where I is the moment of inertia of the fly wheel and ω is the angular velocity.
So this comes down to finding the value of I that gives the required energy. We know the mass is 101kg. The formula for a solid cylinder's moment of inertia is
I = (1/2)mR²
We want (1/2)Iω² = 7.2e8 J and we know ω is limited to 470 revs/sec. However, ω must be in radians per second so multiply it by 2π to get
ω = 2953.1 rad/s
Now let's use this to solve the energy equation, E = (1/2)Iω², for I:
I = 2(7.2e8 J)/(2953.1 rad/s)² = 165.12 kg·m²
Now find the radius R,
165.12 kg·m² = (1/2)(101)R²,
√(2·165/101) = 1.807m
R = 1.807m
Answer:
Part i)
h = 5.44 m
Part ii)
h = 3.16 m
Explanation:
Part i)
Since the ball is rolling so its total kinetic energy in this case will convert into gravitational potential energy
So we have
here we know that for spherical shell and pure rolling conditions
Part b)
If ball is not rolling and just sliding over the hill then in that case
