An ancient wooden club is found that contains 280g of carbon and has an activity of 7.3 decays per second.

Determine its age assuming that in living trees the ratio of ¹⁴C/¹²C atoms is about 1.3

A juniper-wood plank measuring 0.31 ft by 1 ft by 17 ft is totally submerged in water.

(a) What is its weight?

(b) What is the buoyant force acting on it?

(c) What is the size and the direction of the net force on it?

size

direction

An antelope is at a distance of 20.0 m from a converging lens of focal length 27.0 cm. The lens forms an image of the animal.
(a) If the antelope runs away from the lens at a speed of 4.10 m/s, how fast does the image move? mm/s

Three charges are placed on the y-axis. The first, with charge 8nC, sits at y=5cm. The second, with charge -14nC, is at y=0cm. The third, -10nC, is at y=−5cm.

a) What is the electric potential on the x-axis at x=10cm?

b) What is the magnitude of the electric field at x=10cm?

c) What is the electric potential at x= −10cm?

d) What is the magnitude of the electric field at x= −10cm?

Example #2A block with mass m = 5 kg sits on a surface with a coefficient of static friction sk= 0.5 and a coefficient of kinetic friction uk= 0.3. a)If you can pull on the block at any angle, what minimum force is required to break static friction and cause the block to slide? b)What is the optimal angle to pull at? c)If you pull at the optimal angle with the minimum force, what will the acceleration of the block be once static friction is broken?

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 2.0-kg object at the origin of the coordinate system, a 6.0-kg object at (0, 2.0), and a 11.0-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin.

Please show all work! thanks!

A 80.0 cm long guitar string has mass of 75.0g and it is kept taut with force of tension equal to 800N.

 Determine: (1) speed of propagation of a transverse wave in this string, (2) frequency of the fourth harmonic (of a transverse standing wave on this string), and (3) wavelength of the fourth harmonic.

Sketch the fourth harmonic normal mode.

 How many nodes (N) and antinodes (A) are in the fourth harmonic? Label them above.

 If incident wave has the amplitude of 5.5 cm, what is the amplitude of the standing wave?

 If the reflected wave has a vertical displacement of +2.3 cm (at some time instant) at the left end of the string, what is the vertical displacement (at the same time instant) of the incident wave at the same end of the string?

A machine part has the shape of a solid uniform sphere of mass 220 g and diameter 2.90 cm . It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point.

Part A

Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.

Part B

How long will it take to decrease its rotational speed by 19.0 rad/s ?

Compare Einstein's, Classical and Debye's theories of heat capacity.

An otter jumps horizontally off a cliff with a speed of 2.72 m/s and lands in the water a horizontal distance of 4.67 m from the edge of the cliff. How high above the water did the otter jumps from?

_________ m

An 8-ton truck is initially going up a 20° ramp with a speed of 90 km/hr. The truck, then, brakes reaching a speed of 36 km/hr after 3 seconds. Assuming constant deceleration determine (a) the magnitude of the braking force, (b) the additional time required for the truck to stop. Neglect air resistance and rolling resistance

Explain the relationship between magnetism and current. How are magnets and electric charges similar? How are they different? What is something new you learned about electricity and magnetism?

An Atwood's machine consists of blocks of masses m₁ = 9.1 kg and m₂ = 20.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 8.00 kg and radius r = 0.200 m. The block of mass m₂ is allowed to drop, and the cord turns the pulley without slipping.

a) Why must tension T2 be greater than T1

B) what is the acceleration of the system assuming there is no friction

C) Tension in T1=

Tension in T2=