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Answer:
The change in gravitational potential energy is -1.80x10⁵ J.
Explanation:
The change in gravitational potential energy is given by:
Where:
"i" is for final and "f" for final
m: is the mass
g: is the gravity = 9.81 m/s²
h: is the height
For the car and the passengers we have:
The minus sign is because when the elevator car and the passengers are up they have a bigger gravitational potential energy than when they are in the ground.
Therefore, the change in gravitational potential energy is -1.80x10⁵ J.
I hope it helps you!
Answer:
h >5/2r
Explanation:
This problem involves the application of the concepts of force and the work-energy theorem.
The roller coaster undergoes circular motion when going round the loop. For the rider to stay in contact with the cart at all times, the roller coaster must be moving with a minimum velocity v such that at the top the rider is in a uniform circular motion and does not fall out of the cart. The rider moves around the circle with an acceleration a = v²/r. Where r = radius of the circle.
Vertically two forces are acting on the rider, the weight and normal force of the cart on the rider. The normal force and weight are acting downwards at the top. For the rider not to fall out of the cart at the top, the normal force on the rider must be zero. This brings in a design requirement for the roller coaster to move at a minimum speed such that the cart exerts no force on the rider. This speed occurs when the normal force acting on the rider is zero (only the weight of the rider is acting on the rider)
So from newton's second law of motion,
W – N = mv²/r
N = normal force = 0
W = mg
mg = ma = mv²/r
mg = mv²/r
v²= rg
v = √(rg)
The roller coaster starts from height h. Its potential energy changes as it travels on its course. The potential energy decreases from a value mgh at the height h to mg×2r at the top of the loop. No other force is acting on the roller coaster except the force of gravity which is a conservative force so, energy is conserved. Because energy is conserved the total change in the potential energy of the rider must be at least equal to or greater than the kinetic energy of the rider at the top of the loop
So
ΔPE = ΔKE = 1/2mv²
The height at the roller coaster starts is usually higher than the top of the loop by design. So
ΔPE =mgh - mg×2r = mg(h – 2r)
2r is the vertical distance from the base of the loop to the top of the loop, basically the diameter of the loop.
In order for the roller coaster to move smoothly and not come to a halt at the top of the loop, the ΔPE must be greater than the ΔKE at the top.
So ΔPE > ΔKE at the top. The extra energy moves the rider the loop from the top.
ΔPE > ΔKE
mg(h–2r) > 1/2mv²
g(h–2r) > 1/2(√(rg))²
g(h–2r) > 1/2×rg
h–2r > 1/2×r
h > 2r + 1/2r
h > 5/2r
The best and most correct answer among the choices provided by your question is the third choice or letter C.
<span>The statement "Your hypothesis must be testable." is true about the scientific process.
</span>I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
First Order Neurons
Explanation:
First Order Neurons
The main function of First Order Neurons is to deliver sensory information from sensory receptors to the spinal cord.
In Actual there are three orders of neurons, the first order neuron carry signals from periphery to the spinal chord, the second order neuron carry signal from from spinal chord to the thalamus. And the third order neurons carry signals to the primary sensory cortex.
