The length of a simple pendulum is 0.84 m and the mass of the particle (the "bob") at the end of the cable is 0.23 kg. The pendulum is pulled away from its equilibrium position by an angle of 9.05° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion.

A bungee jumper of mass 110 kg jumps from a cliff of height 120m. The massless relaxed bungee cord has a length of 15 m. Ignore the height of the body of the jumper. K=125N/m. (a) Find the velocity of the jumper right before the bungee starts to stretch. (b) Find the distance the cord stretches.

Please explain the steps. Thank you!

An electron is confined by some potential energy well centered about the origin, and is represented by the wave function ψ(x) = Axe−x2/L2, where L = 4.48 nm. The electron's total energy is zero. (a) What is the potential energy (in eV) of the electron at x = 0? eV (b) What is the smallest value of x (in nm) for which the potential energy is zero? nm

In the homework, you were asked to calculate the minimum height needed for a roller coaster car to just barely make a circular loop-the-loop. Instead, suppose a roller coaster designer wants the riders to feel their seats pushing back on them with a force equal to their weight when the car is at the inside, top of the loop. What height h should the car be released from if this condition is to be met? Express your answer in terms of R. Ignore friction.  
a. After drawing a free body diagram for a person in the car when the car is at the inside, top of the loop, determine a constraint equation on the square of the speed when the car is at that position. b. Apply conservation of energy to determine the necessary, minimum height h. Express your answer in terms of the radius R of the loop.

2. A rigid disk with radius 2 m is spinning at an angular speed of 8 1/s (or 8 rad/s). A constant angular acceleration is applied that slows downthe disk at a rate of 2 1/s²(or 2 rad/s²).

(i) Calculate the number of revolutions the disk does before coming to a full stop.

(ii) Calculate the centripetal acceleration of a point, positioned at 1 m from the disk rotation axis, at t = 2 s.

(iii) Calculate the tangent speed of a point positioned at the edge of the disk at t = 2 s.

Q: In an elastic collision between two bodies of equal mass, with body 2 initially at rest, body 1 moves off at angle θ relative to the direction of its initial velocity and body 2 at angle φ. The sine of the sum of θ and φ, sin(θ + φ), is equal to.....................

Question options:

a). 0.

b). 0.500.

c). 0.707.

d). 0.866.

e). 1.00.

=> I tried but it's not A or D so maybe someone can help.

=> Answer left is B, C, E

A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00 s. If the diameter of the tire is 58.0 cm, find (a) the number of revolutions the tire makes during the motion, assuming that no slipping occurs. (b) What is the final angular speed of a tire in revolutions per second?                                          

Answer:  (54.3 rev, 12.1 rev/s) --> please show me how to get this answer!

1.The terms H II and H2 are both pronounced “H two.” What is the difference in meaning of those two terms? Can there be such a thing as H III?

2. Why do nebulae near hot stars look red? Why do dust clouds near stars usually look blue?

3. Describe the characteristics of the various kinds of interstellar gas (HII regions, neutral hydrogen clouds, ultra-hot gas clouds, and molecular clouds).

4. Describe how the 21-cm line of hydrogen is formed. Why is this line such an important tool for understanding the interstellar medium?

5. Describe the properties of the dust grains found in the space between stars.

6. Why do molecules, including H2 and more complex organic molecules, only form inside dark clouds? Why don’t they fill all interstellar space?

7. Why can’t we use visible light telescopes to study molecular clouds where stars and planets form? Why do infrared or radio telescopes work better?

8. The 21-cm line can be used not just to find out where hydrogen is located in the sky, but also to determine how fast it is moving toward or away from us. Describe how this might work.

9. Astronomers recently detected light emitted by a supernova that was originally observed in 1572, just reaching Earth now. This light was reflected off a dust cloud; astronomers call such a reflected light a “light echo” (just like reflected sound is called an echo). How would you expect the spectrum of the light echo to compare to that of the original supernova?

10. We can detect 21-cm emission from other galaxies as well as from our own Galaxy. However, 21-cm emission from our own Galaxy fills most of the sky, so we usually see both at once. How can we distinguish the extragalactic 21-cm emission from that arising in our own Galaxy? (Hint: Other galaxies are generally moving relative to the Milky Way.)

Cart 1 amd 2 are now moving toward each other when they collide and stick together. Cart 1 has a mass of 500g (.5kg) and is travelling at a speed of 0.30m/s to the right. Cart 2 has a mass of 350g (.35kg) and is travelling at a speed of 0.55m/s to the left.

A) What is their velocity (speed and direction) after the collision?

B) What % of the initial KE is lost in the collision?

Please show all work, thank you!

We assumed that the spring is ideal. In reality, as you stretch and compress the spring, frictional forces of the spring come into play. Explain how the frictional forces of the spring would or could affect your measurements.

A small loop of copper wire is inside and held perpindicular to a large, uniform magnetic field. You move the loop in circles and vary the speed. What do you observe?

As a quarterback throws the football, it leaves his hand at a height of h and at an initial speed of v0 at an angle θ above the horizontal. The receiver can’t get to the football in time and it falls onto the field. What is the ball’s speed as it hits the ground? Solve this problem in two ways: (a) using kinematics, explicitly calculating the trajectory the ball takes (b) using conservation of (kinetic + potential) energy

Explain why the sine and logarithm of 1 meter are not well-defined.

Consider an ideal massless rubber-band which has an upstretched ‘l’. A roll of 50 pennies of total mass m_pis attached to the rubber band. The new stretched length of the rubber band with the pennies hanging down from the end of the rubber band is 1:

Assume the rubber band satisfies Hookes’ law when it is stretched, what is the spring constant of the rubber band?

A small nut with mass with the mass m_nis then attached to the rubber band and both are rotated by a motor at an unknown constant frequency f. The rubber band is stretched to a length ‘l’.

Find an expression for the frequency

How long does it take for the nut to complete one rotation?

What is the angular frequency of the nut?