In the picture a man climbs a ladder leaning at 500 abpve the horizontal. The static friction coefficient between the ladder and ground is .6, the ladder is 3 meters long and weighs 100 newtons. If the man weighs 700 N, how far up the ladder can he climbs without the ladder sliding out from under him? (Assume no friction between the wall and ladder)

A square rod of length L0 = 2.45m and sidelength d = 6.78cm is compressed with a force of |Fc| = 90.8N in the direction of the long axis. (a) What is the magnitude of the scalar tensile stress? (b) If we assume that the area of the square rod is approximately constant and its final resting length is L = 2.35m, then what is the Young's modulus of the square rod? Now assume that the rod is stuck between two slabs that are separated by the sidelength of the rod. (c) What is the shear stress when the magnitude of the force of the top slab on the square rod in the direction of the long axis of the rod is |Fs| = 73.8N? (d) If the total distance that the top of the rod moved, as compared to the bottom of the rod, is ?x = 0.206cm, then what is the shear modulus of the rod in this geometry?

How tall must a water-filled manometer be to measure blood pressures as high as 300 mm Hg?

A cookie jar is moving up a 40° incline. At a point 55 cm from the bottom of the incline (measured along the incline), the jar has a speed of 1.8 m/s. The coefficient of kinetic friction between jar and incline is 0.15.

(a) How much farther up the incline will the jar move?
___ m

(b) How fast will it be going when it has slid back to the bottom of the incline?
___m/s

A 3.0 kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0 kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0 kg cart is moving to the left with a speed of 1.0 m/s.

a. What is the final velocity of the 5 kg cart?

b. Determine the speed of the center of mass of the two carts before and after the collision.

c. If instead, the two carts stuck together after the collision, what would be their common velocity?

d. Determine the amount of kinetic energy lost in the collisions described in (a) and (c). State the type of collision in parts (a) and (c) and suggest a reason for the loss of total energy after the collision.

The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (the figure (Figure 1)). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the departure planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet.

a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about from a flight from Mars to the earth?Explain.

b) How long does a one-way trip from the the earth to Mars take, between the firings of the rockets?

c) To reach Mars from the earth, the launch must be timed so that Mars will be at the right spot when the spacecraft reaches Mars's orbit around the sun. At launch, what must the angle between a sun-Mars line and a sun-earth line be?.

a) Calculate the wavelength of x ray emitted when 35-keV electron collies with on molybdenum target.

b) A single electron orbiting a hydrogen nucleus moves from energy level E₄ to E₂. Calculate the energy in joules of the photon emitted due to this energy change.

c)As an electron orbits the nucleus, it can be thought of as a standing wave. Calculate the frequency of the wave if the electron is in the 4^th energy level of hydrogen atom

A 14 mm high object is 11 cm from a concave mirror with focal length 16 cm. Calculate (a) the location of the image, (b) the height of the image, and (c) the type of image.

Three polarizing disks whose planes are parallel and centred on common axis. The directions of their transmission axes relative to the vertical are respectively: θ₁ = 34^o clockwise, θ₂ = 16^o counter-clockwise, and θ₃ = 19^o clockwise. A beam of light polarized along the vertical is incident onto the first polarizer with an intensity of I₀ = 30 W/m². Calculate the transmitted intensity through all three polarizers.

The cornea, a boundary between the air and the aqueous humor, has a 3.0 cm focal length when acting alone.

What is its radius of curvature?

A) The emissivity of the human skin is 97.0 percent. Use 35.0 °C for the skin temperature and approximate the human body by a rectangular block with a height of 1.84 m, a width of 30.0 cm and a length of 24.0 cm. Calculate the power emitted by the human body.

B) Fortunately our environment radiates too. The human body absorbs this radiation with an absorbance of 97.0 percent, so we don't lose our internal energy so quickly. How much power do we absorb when we are in a room where the temperature is 23.5 °C?

C) How much energy does our body lose in one second?

The primary optical element of the Hubble Space Telescope (HST) is 3.2 m in diameter and has a focal length of 62 m. (Treat it as a simple, single lens for this homework) The telescope is aimed at Jupiter and the collected light is focused onto a sensitive Charge Coupled Device (CCD) detector, similar to what is in a digital camera. Each pixel in the detector is a 21 μm x 21 μm square, and the full CCD is 4096 x 4096 pixels. Thus the CCD is about one square inch in size. The HST is in orbit very close to the Earth (compared to other distances in the Solar system).

Look up the size of Jupiter and the distance to Jupiter when it is closest to Earth. Use the lens formula to determine the magnification of the image Hubble takes.

How many pixels in diameter is Jupiter’s image on the CCD?

Given this CCD, what is the smallest feature on Jupiter you would expect to be able to resolve? (Another way of thinking about that question is: How large a square on the surface of Jupiter does one pixel in the image represent?)

(eye piece parameters are not given for this question but it can be solved without them)