Two vectors are given by A= 1.5i+6.6j and B= 7.0i+6.2j. Find (1) (A+B)*B and (2) the component of A along the direction of B?

A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 5.4 m. The total mass of the empty balloon and basket is mb = 121 kg and the total volume is Vb = 0.062 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.079 m3.

volume of helium in the balloon when fully inflated? :660

magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium. : 2352

buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium. :8287

1)What is the magnitude of the force of gravity on each person?

2)What is the magnitude of the buoyant force on each person?

3)How many FULL people can the balloon lift up? (Your answer must be an integer.)

Problem 2.

Mass of Mars- 6.39 x 10^23 kg

Mass of Earth- 5.972 x 10^24 kg

Mass of Sun- 1.989 x 10^30 kg

Distance between earth and sun- 1.496 x 10^11

Distance between earth and mars- 5.46 x 10^7

a) What is the force of gravity on earth due to mars?

b) What is the force of gravity on mars due to earth?

c) What is the force of gravity on earth due to the sun?

d) Why does earth revolve around the sun instead of mars?

A student in our class is confused about the motion of pulses on a long taut spring and has scored zeros on many of the homework problems. Pick two ideas that you think are critical for understanding this topic. State them clearly and describe how you would help your fellow student make sense of these ideas. Note: This is an essay question. Your answer will be judged not solely on its correctness, but for its depth, coherence, and clarity.

Part A) When monochromatic UV light of wavelength 347 nm is sent through a diffraction grating, the first order maximum occurs at 17.9^o. How many lines per cm are in the grating?

Part B) Through what voltage should an electron be accelerated from rest so that it would produce the same interference pattern as this light.

Please answer both parts and show work.

A proton moves from a location where V =75 V to a spot whereV = -20 V.

(a) What is the change in the proton's kinetic energy?

(b) If we replace a proton with an electron, what is the change in kinetic energy?

1. A street light is supported by two wires and each makes a different angle from each other. The one on the left is 32 degrees from the vertical and the one on the right is 43 degrees from the vertical. Find the tension in each wire if the street light has a mass of 60.0 kg. See notes in week 5 announcement on this problem.

2. There are three masses m₁ = 2.0 kg, m₂ = 5.0 kg and m₃ = 7.0 kg. The mass are all affixed to a massless rod of length 15cm. m₁ and m₃ are at the ends and m₂ is 10 cm from left where m₁ is. Calculate the center of mass of the system and specify from which end it is from.

3. A pair of hedge trimmers are 45 cm long from the pivot to the end of the handles. If the person applies of a force of 15 N on each handle and the blades are 3.5 cm long, how much force is applied to the branch?

4. A 245 kg person lays on board that is supported only on the ends and that has a mass of 12.0 kg. If the person and the board are both 205 cm long and the person

Problem 3: Astronaut testing At its Ames Research Center, NASA uses its large 20-G centrifuge to test the effects of very large accelerations (hypergravity) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and the astronaut is strapped in at the other end. Suppose that he is aligned along the arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this machine is typically 12.5g.

a) How fast must the astronauts head be moving to experience this maximum acceleration?

b) What is the angular velocity ω of the arm?

c) What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?

Suppose the electric field between the electric plates in the mass spectrometer of the figure 20-39 in the textbook is 2.69×104V/m and the magnetic fields B=B′=0.70T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by 1.67 ×10−27kg.)

A - How far apart are the lines formed by the singly charged ions of mass numbers 12 and 13 on the photographic film?

Express your answer using two significant figures.

r12 and 13 = ? m

B- How far apart are the lines formed by the singly charged ions of mass numbers 13 and 14 on the photographic film?

Express your answer using two significant figures.

r13 and 14 = ? m

C- What if the ions were doubly charged?

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

r12 and 13, r13 and 14 = ? m

A 3.10 g bullet moving at 270 m/s enters and stops in an initially stationary 2.30 kg wooden block on a horizontal frictionless surface.

a) What's the speed of the bullet/ block combination?

b) What fraction of the bullet's kinetic energy was lost in this perfectly inelastic collision?

c)How much work was done in stopping the bullet?

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s² lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s² lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.39 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 1.8 mm. If the floor is carpeted, this stopping distance is increased to about 1.1 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.

A 557-N physics student stands on a bathroom scale in an 859-kg (including the student) elevator that is supported by a cable. As the elevator starts moving, the scale reads 496 N

Find the direction of the acceleration of the elevator.

What is the acceleration if the scale reads 682 N ?

If the scale reads zero, should the student worry? Explain.

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

3800 Character(s) remaining

What is the tension in the cable in part A?

What is the tension in the cable in part D?

1. Two particles having charges of 0.570 nC and 20.5 nC are separated by a distance of 1.20 m .

a) At what point along the line connecting the two charges is the net electric field due to the two charges equal to zero?(Express your answer in meters.)

b)Where would the net electric field be zero if one of the charges were negative?(Enter your answer as a distance in meters from the charge initially equal to 0.570 nC .)

c)Is this point between the charges? Yes or No

2. A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 19.0 cm , giving it a charge of -13.0 μC .

a) Find the electric field just inside the paint layer. (Express your answer in newtons per coulomb.)

b) Find the electric field just outside the paint layer. (Express your answer in newtons per coulomb.

c) Find the electric field 6.50 cm outside the surface of the paint layer. (Express your answer in newtons per coulomb.)