A bead slides without friction around a loop–the–loop (see figure below). The bead is released from rest at a height h = 3.60R.
(a) What is its speed at point ? (Use the following as necessary: the acceleration due to gravity g, and R.)
v =
So I can't get this. I know the form of a would be sqrt((number)*g*R) but how do you get the number?
An electric scooter has a battery capable of supplying 130 Wh of energy. If friction forces and other losses account for 60.0% of the energy usage, what altitude change can a rider achieve when driving in hilly terrain, if the rider and scooter have a combined weight of 820 N?
i got this to be 342.44 by doing .6*130*3600=280800J then 280800=h*820. whats wrong in this case?
The fraction of the 130 Watthours used to increase potential energy is 40%, not 60%.
60% is the loss fraction.
ooh I see! Thank you! Would you be able to help with the first one?
Not without the "figure below" which was not provided.
To determine the speed of the bead at point A, we can use the principle of conservation of mechanical energy. At point A, the bead has only gravitational potential energy, which is then converted into kinetic energy as it moves to the bottom of the loop.
The total mechanical energy remains constant throughout the motion, so we can equate the initial potential energy at height h to the final kinetic energy at point A. Mathematically, we have:
mgh = (1/2)mv^2
where m is the mass of the bead, g is the acceleration due to gravity, h is the initial height, and v is the speed at point A.
Since the mass of the bead cancels out, we can simplify the equation to:
gh = (1/2)v^2
Solving for v, we get:
v = sqrt(2gh)
Substituting h = 3.60R and g as the acceleration due to gravity, we can calculate v as follows:
v = sqrt(2 * g * h)
v = sqrt(2 * g * 3.60R)
So, the speed at point A is given by v = sqrt(2g * 3.60R).
Regarding the second question about the electric scooter, let's go through the calculations step by step. The energy supplied by the battery is 130 Wh, but since friction forces and other losses account for 60.0% of the energy usage, only 40.0% of the energy is available for altitude change.
To find the available energy, we multiply the total energy by the percentage:
Available Energy = 0.40 * 130 Wh
Available Energy = 52 Wh
Now, let's convert this energy from watt-hours to joules. We can use the conversion factor of 1 Wh = 3600 J:
Available Energy = 52 Wh * 3600 J/Wh
Available Energy = 187,200 J
Next, we can use the formula for gravitational potential energy:
Potential Energy = weight * height
We are given that the weight is 820 N, and we need to find the altitude change (height). Rearranging the formula, we get:
height = Potential Energy / weight
Substituting the values, we have:
height = 187,200 J / 820 N
height ≈ 228.29 meters
Therefore, the altitude change the rider can achieve when driving in hilly terrain is approximately 228.29 meters.