I hope I'm not too late.
GPE = mass * gravity * height
GPE = 2 kg * 9.8 m/s * 10
GPE = 196 Joules
Answer:
0.181
Explanation:
We can convert the 0.5 rps into standard angular velocity unit rad/s knowing that each revolution is 2π:
ω = 0.5 rps = 0.5*2π = 3.14 rad/s
From here we can calculate the centripetal acceleration
Using Newton 2nd law we can calculate the centripetal force that pressing on the rider, as well as the reactive normal force:
Also the friction force and friction acceleration
For the rider to not slide down, friction acceleration must win over gravitational acceleration g = 9.81 m/s2:
Answer:
The hill should be not less than 0.625 m high
Explanation:
This problem can be solved by using the principle of conservation of mechanical energy. In the absence of friction, the total mechanical energy is conserved. That means that
is constant, being U the potential energy and K the kinetic energy


When the car is in the top of the hill, its speed is 0, but its height h should be enough to produce the needed speed v down the hill.
The Kinetic energy is then, zero. When the car gets enough speed we assume it is achieved at ground level, so the potential energy runs out to zero but the Kinetic is at max. So the initial potential energy is transformed into kinetic energy.

We can solve for h:

The hill should be not less than 0.625 m high
Answer:
The resistance of each resistor is 2.5 Ω
The potential difference across each resistor is 2.4 V.
Explanation:
By Ohm's law,
<em>V </em>=<em> IR</em>
where <em>V</em> is the potential difference or voltage across an element, <em>I</em> is the current flowing through it and <em>R</em> is its effective resistance.
For the group of five resistors, let their combined resistance be <em>R</em>.
Then
(12.0 V) = (0.961 A)(<em>R</em>)

Because they are in series, <em>R</em> is the arithmetic sum of their individual resistances. Because they are all identical, the resistance of each resistor is

Also, because they are in series and are equal, the EMF is distributed across them equally. Therefore, the potential difference across each resistor is
