Answer:
0.3677181864 m
Explanation:
u = Velocity = 1.5 m/s
= Angle = 20°
y = -20 cm
Velocity components


Acceleration components




Time taken is 0.26088 seconds

The distance the beetle travels on the ground is 0.3677181864 m
Hey! I empathize with you, as I just started the energy unit in physics as well!
Alright, lets list what we know, and which equation(s) we need.
PE = Gravitational Potential Energy

m = mass
g = gravity (9.8 m/s^2)
h = height
Guess what?
We need to find the height!
Lets make this more organized:
Known:
m = 40 kg
PE = 14000
g = 9.8 m/s^2
Unknown:
h = ?
================================
Now, if we take a look at the equation PEg = mgh, you will see that we have everything besides the height! So lets solve for the height by substituting in for the variables we know:
14000 J = 40 kg * (9.8 m/s^2) * h
40 * 9.8 = 392
14000 J = 392 * h
14000/392 = h
35.71 m = h
There we go! If you simply list what you know and don't know, you will find the equation you need to solve the problem.
Have a great day and good luck!
Answer:
The equation of equilibrium at the top of the vertical circle is:
\Sigma F = - N - m\cdot g = - m \cdot \frac{v^{2}}{R}
The speed experimented by the car is:
\frac{N}{m}+g=\frac{v^{2}}{R}
v = \sqrt{R\cdot (\frac{N}{m}+g) }
v = \sqrt{(5\,m)\cdot (\frac{6\,N}{0.8\,kg} +9.807\,\frac{kg}{m^{2}} )}
v\approx 9.302\,\frac{m}{s}
The equation of equilibrium at the bottom of the vertical circle is:
\Sigma F = N - m\cdot g = m \cdot \frac{v^{2}}{R}
The normal force on the car when it is at the bottom of the track is:
N=m\cdot (\frac{v^{2}}{R}+g )
N = (0.8\,kg)\cdot \left(\frac{(9.302\,\frac{m}{s} )^{2}}{5\,m}+ 9.807\,\frac{m}{s^{2}} \right)
N=21.690\,N
You should put when you will leave, where you will be, and what time you will get back.