​​​​​Explain the principle and construction of a hydrometer. What is the purpose of the common measurements of the specific gravities of an automobile’s radiator coolant and battery electrolyte?

The potential energy shared by two atoms separated by a distance r in a diatomic molecule is given by the Lennard-Jones function (?0 and ?0 are constants): ?(?) = ?0 [( ?0/?)^12 − 2( ?0/? )^6 ] (a) Where is ?(?) = 0? (b) Show that the minimum potential energy is −?0 and that it occurs at ?0. (c) Where is ?? = 0 ? (d) Sketch ?(?).

Questions for my lab:

What is the significance of the observation of discrete spectral lines in the emission spectrum of hydrogen?

What is the possible effects due to the adjustment of the spectrometer in a hydrogen spectrum?

What is the possible effects due to the orientation of the grating in a hydrogen spectrum? Thanks

In the Olympic shot-put event, an athlete throws the shot with an initial speed of 12.0m/s at a40.0? angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground

A.How far does the shot travel?

B. Repeat the calculation of the first part for angle 42.5

C. Repeat the calculation of the first part for angle 45

?

D. Repeat the calculation of the first part for angle 47.5

?

E. At what angle of release does she throw the farthest
?

1.                             Celeste Orion, an assistant coach for The Vanishing Planet Soccer Team has been asked to evaluate each of the team’s players to determine which players kick with the highest velocity. Celeste borrows a radar gun from her friend Pluto. She gathers the players together and asks them to stand at the penalty mark and kick the ball into the goal as hard as they can. She tells them that the ball must go into the goal for it to be considered “legal”. She stands, dead center behind the goal, holds the radar gun 4 ft off the ground and points it directly at the penalty mark (slightly downward). She gives each player 3 “legal” kicks and records the highest speed.

The following information may help you answer this question: 1) The radar gun works by sending a “radar” signal (on a straight line) in the direction that it is pointed. The signal then bounces off the object and returns (on a straight line) back to the gun. The change in the rate of the signal return to the radar gun is used to determine ball velocity. 2) You may look online for the term “cosine effect” in the context of a radar gun.

a. From a purely biomechanical standpoint, explain the limits to her strategy.

b. Give a mathematical example that illustrate the limitations.

c. Identify a simple strategy (or strategies) that she might use to improve her analysis.

What is the difference between static and kinetic friction. Define both, write their SI unit and dimension. Write down the mathematical statement (formula) that allows us to calculate the force of friction. Explain each term with its unit. Let’s say you’re dragging a 50 kg rubber box on wetconcrete. How do you calculate the force of friction on this box?

Consider an old-fashioned bicycle with a small wheel of radius 0.51 m and a large wheel of radius 0.8 m. Suppose the rider starts at rest, accelerates with a constant acceleration for 8 minutes to a velocity of magnitude 24.5 m/s. He maintains his velocity for 9.5 minutes and then decelerates, with constant deceleration, for 7.3 minutes. Find the total angle through which a point on the small wheel has turned.

A transverse sinusoidal wave on a string is moving in the −x-direction. Its speed is 30.0 m/s, and its period is 20.0 ms. At t = 0, a colored mark on the string at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.30 m/s. (a) What is the amplitude of the wave (in m)? 0.0204 Correct: Your answer is correct. m (b) What is the phase constant (in rad)? Incorrect: Your answer is incorrect. Use the expressions you wrote for y and vtransverse from part (a), and divide them to find an equation for tan(ϕ). Take the inverse to find ϕ. Note that the angle you are looking for is in the second quadrant, so you will need to modify your calculator answer as needed. rad (c) What is the maximum transverse speed of the string (in m/s)? m/s (d) Write the wave function for the wave. (Use the form A sin(kx + ωt + ϕ). Assume that y and x are in m and t is in s. Do not include units in your answer.) y(x, t) = m

1. A 1.5- volt battery is connected across an LED bulb, but the bulb does not “light up.” What are two possible reasons why it’s not lighting? (Both the battery and LED are in working order,)

2. ) In what way are an LED and a solar cell alike? In what ways are they different

Please explain everything in detail, I have a lot of difficulty with science. Thank you!

A 2.0-kg ball moving at 10 m/s makes an off-center collision with a 3.0-kg ball that is initially at rest. After the collision, the 2.0-kg ball is deflected at an angle of 30° from its original direction of motion and the 3.0-kg ball is moving at 4.0 m/s. Find the speed of the 2.0-kg ball and the direction of the 3.0-kg ball after the collision.
Hint: sin²θ + cos²θ = 1.

speed of 2.0-kg ball	m/s
direction of 3.0-kg ball	° from original direction of motion

Lions can run at speeds up to approximately 80.0 km/h. A hungry 106 kg lion running northward at top speed attacks and holds onto a 37.5 kg Thomson's gazelle running eastward at 77.5 km/h.

Find the final speed ?f of the lion‑gazelle system just after the lion attacks.

Find the angle ?θ between the final velocity of the lion‑gazelle system and the East axis, with positive angles measured counterclockwise from the East axis.

An old Biblical story tells of David, a small warrior engaged in man-to-man combat with Goliath, a much larger adversary. In the story, David uses a sling to increase the speed of a projectile (in this case a rock), striking Goliath in the forehead and killing him. The type of sling often used in such combat consists of a long strip of cloth with a pouch halfway down its length. The rock is positioned in the pouch, with the warrior holding both ends of the sling. By whirling the sling in a horizontal* circle, a warrior can release one end of the sling, therefore allowing the projectile to fly in a straight line at high speed. In this problem, we will assume that the sling, when unfolded, was roughly 5.12 feet in total length. We will also assume the rock weighed a half a pound. If David whirled the sling to the point where the sling subtended an angle of θ = 3.93o with the horizontal, with what speed did the rock strike Goliath? (Assume no air friction and that the drop in height due to gravity is minimal.)

speed rock struck Goliath = ______ mph

A typical break shot in pool (the opening shot) is about 20 mph with a ball that is about half the weight of the rock in the story. Considering this, what impact do you think a half-pound rock traveling at the above calculated speed would have on someone if struck in the forehead?

-a- The impact would hurt a little but would likely not cause any injury.

-b- The impact would likely cause serious injury.

Suppose David had missed. How far would the rock travel before striking the ground if David released it from a height of 4.25 ft? (Assume no air friction.)

A rod of length 22.00 cm has linear density (mass per length) given by

λ = 50.0 + 16.0x

where x is the distance from one end, and λ is measured in grams/meter.

(a) What is its mass? _______________g

(b) How far from the x = 0 end is its center of mass? ________________m

gedananken-experiment. explain thebehavior of a yo-yo in terms of conservation of mechanical energy