In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45∘ angle. Suppose a projectile of mass m is launched with speed v0 into a headwind that exerts a constant, horizontal retarding force F⃗ wind =−Fwindi^.

By what percentage is the maximum range of a 0.600 kg ball reduced if Fwind = 0.100 N ?

Express your answer with the appropriate units.

A rope of negligible mass hangs vertically on each side of a pulley. The pulley, which has mass 1.00 kg and radius 20 cm, can be modeled as a thin uniform cylinder. One end of the rope is tied to a box of mass 10.00 kg; this box is resting on the ground. The other end of the rope dangles freely. Then a 15.00 kg monkey, who is initially standing on a ledge 2.00 m above the floor, grabs the freely hanging rope and (starting from rest) accelerates down to the ground. As the monkey descends, the box rises. What is the monkey's speed when it reaches the floor?

A small solid sphere of mass M₀, of radius R₀, and of uniform density ρ₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

R F U R or U F or U R or F or U  The new sphere has radius R < R₀ and mass M = M₀

R F U R or U F or U R or F or U  The new sphere has mass M = M₀ and density ρ < ρ₀

R F U R or U F or U R or F or U  The new sphere has radius R = R₀ and mass M > M₀

R F U R or U F or U R or F or U  The new sphere has density ρ = ρ₀ and radius R < R₀

R F U R or U F or U R or F or U  The new sphere has density ρ < ρ₀ and radius R > R₀

R F U R or U F or U R or F or U  The new sphere has density ρ = ρ₀ and radius R > R₀

Use chemical potentials to explain the driving force for the spontaneous mixing of gases or liquids

A flywheel with a radius of 0.390 m starts from rest and accelerates with a constant angular acceleration of 0.670 rad/s2. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0 ∘. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 120 ∘.

Starting from the one-dimensional motion equation x=Xo + vt

prove that v^2 = Vo^2 + 2a(X-Xo)

If you could eplain as well why/ how each step in the problem proves the equation, this would be greatly helpful.

Thank you!

Show that setting the 4-divergence of current four vector equal to zero gives the equation of continuity.

A 960-kg satellite orbits the Earth at a constant altitude of 95-km.

(a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 193 km?


(b) What is the change in the system's kinetic energy?

(c) What is the change in the system's potential energy?

A marble rolls down an incline, and when it’s halfway down it’s going at 1.12 m/s. Find (a) its starting height and (b) its speed at the bottom.

A bucket of water of mass 16.0 kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.320 m with mass 13.0 kg . The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls a distance 10.6 m to the water. You can ignore the weight of the rope.

What is the tension in the rope while the bucket is falling?

Take the free fall acceleration to be g = 9.80 m/s2 .

With what speed does the bucket strike the water?

Take the free fall acceleration to be g = 9.80 m/s2 .

What is the time of fall?

Take the free fall acceleration to be g = 9.80 m/s2 .

While the bucket is falling, what is the force exerted on the cylinder by the axle?

Take the free fall acceleration to be g = 9.80 m/s2 .

1. What were two reasons as to why Rutherford selected alpha-particles for his experiment?

1. From Millikan’s oil drop experiment, what was he value of the voltage that allowed the  drops to obtain terminal velocity?

Two students are discussing how the period of a toy pig flying in a circle depends on

the length of the string.

Student A says: The period depends on the length of the string.

Student B says: The period is independent of the length of the string.

You have the following equipment: flying pig, stand, stopwatch, metre stick, spring

scale, tape measure, strings of different lengths

How would you make an experiment to prove one of the students is correct and the other wrong?

A 80.0 cm3 box contains helium at a pressure of 2.50 atm and a temperature of 110 ∘C. It is placed in thermal contact with a 210 cm3 box containing argon at a pressure of 4.20 atm and a temperature of 390 ∘C

What is the final thermal energy of each gas? Ef(He),Ef(Ar)

How much heat energy is transferred, and in which direction?

What is the final temperature?

What is the final pressure in each box?

What is the final temperature?

What is the final pressure in each box? pf(He), pf(Ar) =