An archaeologist finds some ancient jewelry made from bone. The jewelry has a carbon mass of 163 g (HINT: Assume all the carbon is ¹²C and determine the number of atoms) and careful measurements show that the remaining ¹⁴C has a current decay rate of 21 decays/s. Determine the age of the bone (and presumably the jewelry). Remember, the ratio of ¹⁴C to ¹²C when the animal died was 1.3×10^-12 & the half-life of ¹⁴C is 5730 y.
age of bone =

A geologist finds an old rock and wants to determine its age using rubidium-strontium dating. This is possible because ⁸⁷Rb, which has a half-life of 4.75×10¹⁰ y, undergoes β ⁻ decay and becomes ⁸⁷Sr. The geologist determines that the ratio of ⁸⁷Sr to ⁸⁷Rb is 0.289. Assuming there was no ⁸⁷Sr in the rock when it was formed, determine the age of the rock.
age of rock =

Is it possible for the potential energy and kinetic energy to both be maximum at the same moment in time for a bouncing spring? Explain.

An airplane with a speed of 77.1 m/s is climbing upward at an angle of 72.5 ° with respect to the horizontal. When the plane's altitude is 625 m, the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth. (b) Relative to the ground, determine the angle of the velocity vector of the package just before impact

A ball is placed at the top of a hill and then released. After 5 seconds it has a speed of 20 m/s. What is the average acceleration of the ball? A) 10 m/s^2 B) 0 m/s^2 C) 100 m D)5 m/s^2 E) 4 m/s^2

4. A 14000N car traveling at 25m/s rounds a curve of radius 200m. Find the following: a. The centripetal acceleration of the car.   


b. The force that maintains centripetal acceleration.


c. The minimum coefficient of static friction between the tires and road that will allow the car to round the curve safely.

A person pulls a 11-kg toboggan for a distance of 3.5 m on a horizontal sheet of ice (frictionless) with a rope directed 25.0º above the horizontal snowy surface. The tension in the rope is 88 N. There is also a zephyr (soft gentle breeze) in the opposite direction of the motion applying a 11.0 N force.

(a) How much net work is done on the toboggan by ALL the forces acting on it?

(b) If the toboggan starts from rest, how fast is it moving after the 3.5 m distance?

(c) Use Dimensionality sense-making to check the expression you derive in part (b).

A ball enters a frictionless track spiraling upward with a speed vo. The radius of the track is half a meter and it has a pitch (ѳ) of 15°.

(a) If the initial speed of the ball is 12 m/s, how high vertically will it rise?

(b) Compare your answer to part (a) with the height the ball would rise if it had been thrown vertically upward, into freefall, with the same initial speed. Explain your results.

(c) If you wish the ball to make exactly 5 revolutions before momentarily coming to rest, how fast must it initially be moving when entering the spiral track?

(d) What assumptions or simplifications did you make in part (c) about the total distance traveled that leaves your answer very close but not exact (friction is not the answer)? Use Related Quantities in conjunction with Order of Magnitude sense-making to justify your assumptions/simplifications.

A horizontal spring with a spring constant of 190 N/cm is compressed 6.3 cm. A wooden block with a mass of 1.5 kg is placed in front of and in contact with the spring. When the spring is released it pushes the block, which slides on a frictionless horizontal surface for some distance. The block then slides up a frictionless incline of 27 above the horizontal and comes to a momentary stop before sliding back down. The system is the spring, the block, the incline, and the Earth. Ignore air resistance.

A) Sketch the situation and label all variables for: i. the spring and block before the spring is released ii. the block sliding on the horizontal surface iii. the block sliding up the incline

B) List all known quantities.

C) Draw the free body diagram for the block sliding up the incline.

D) What is the potential energy of the spring before it is released?

E) What is the kinetic energy and the speed of the block as it slides on the horizontal surface after the spring has pushed it?

F) At what height does the block stop on the incline?

G) If the incline were rough, how would the stopping height of the block compare to the stopping height when the incline is frictionless? Explain using energy.

People who do very detailed work close up, such as jewelers, often can see objects clearly at a much closer distance than the normal 25.0cm. What is the power of the eyes of a woman who can see an object clearly at a distance of only 8.75cm? Assume a distance from the eye lens to the retina of 2.00cm

power: 61.43diopters -right

What is the size of the image of a 1.50mm object, such as lettering inside a ring, held at this distance? Enter your answer as a positive number if the image is upright and negative if it is inverted.

image size at : −0.23- wrong

What would the size of the image be if the object were held at the normal 25.0cm ?

image size at : −0.34 - wrong

A particle with speed V1= 75 m/s makes a glancing elastic collision with another particle that initially is at rest. Both particles have the same mass. After the collision, the struck particles moves off at an angle that is 45 degrees above the line along V1. The second particle moves off at 45 degree below this line. The speed of the struck particle after the colllision is approximately.

A: 38 m/s

B: 82 m/s

C: 64 m/s

D: 47 m/s

E: 53 m/s

Consider a thin spherical shell located between r = 0.49a₀ and 0.51a₀. For the n = 2, l = 1 state of hydrogen, find the probability for the electron to be found in a small volume element that subtends a polar angle of 0.11° and an azimuthal angle of 0.25° if the center of the volume element is located at: θ=5°, ϕ=35°.

1.Consider a negative point charge. Sketch electric field lines, including their direction.

2 Calculate electric field of 1 electron at a distance of 0.1 nanometer away from it. Express your answer in SI units.

3 Consider a point charge of 1 C and calculate its electric field at a distance of 1 m.