You use a slingshot to launch a potato horizontally from the edge of a cliff with speed υ0. The acceleration due to gravity is g. Take the origin at the launch point. (a) How long after you launch the potato has it moved as far horizontally from the launch point as it has moved vertically? What are the coordinates of the potato at this time? (b) How long after you launch the potato is it moving in a direction exactly 45° below the horizontal? What are the coordinates of the potato at this time?

Through cunning physics trickery I have trapped a point charge Q at the center of a thin-walled hollow conductive sphere of radius R, which itself carries a net charge of -3Q.

a.    How much charge will collect on the inside surface of the hollow sphere?

b.   How much charge will collect on the outside surface of the hollow sphere?

c.    Draw a picture of this arrangement, including a depiction of any electric field lines.

d.   Graph the resulting electric field E as a function of distance from the center, r.

A spring gun fires a bullet of mass m=.04 kg horizontally at a ballistic pendulum apparatus with a mass M=.350. the bullet lodges itself into the pendulum. After collision, the center of mass of the bullet and pendulum rises by .07 meters. What is the approximate initial speed v of the bullet?

- In a cylindrical container with a base area A, there are N monatomic gas particles at temperature T which are ideal. The upper part of the container is closed with a lid which has a weight M and can moves upward and downward without friction . There is vacuum on the lid and the whole system is under gravity.
a) Calculate the balance position of the lid. When performing this calculation, you can assume that the cover is quite narrow in the vertical.

- Suppose the system is completely isolated from the outside, doubling the weight of the lid (2M).
b) Determine the new temperature T* of the gas and the new equilibrium position of the lid.
c) Calculate the change in the entropy of the gas.

Show that the equation v²=v₀² −2g(y−y₀) is dimensionally consistent. (use dimensional analysis)

A solid, homogeneous sphere with a mass of m₀, a radius of r₀ and a density of ρ₀ is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'f or s' are possible answers in some of the cases. (So for each, pick either r, s, or f- or a combo.. thank you)

1. The new sphere has a density of ρ = ρ₀ and a mass of m < m₀.
2. The new sphere has a density of ρ = ρ₀ and a radius of r < r₀.
3. The new sphere has a mass of m = m₀ and a radius of r > r₀.

4. The new sphere has a density of ρ < ρ₀ and a radius of r = r₀.
5. The new sphere has a mass of m = m₀ and a radius of r < r₀.
6. The new sphere has a mass of m > m₀ and a radius of r = r₀.

7. The new sphere has a radius of r < r₀ and a mass of m > m₀.
8. The new sphere has a radius of r < r₀ and a density of ρ > ρ₀.
9. The new sphere has a mass of m > m₀ and a density of ρ < ρ₀.

Movers push an 80 kg trunk at 1.0 m/s when they encounter a 2.5 m long stretch of floor where the coefficient of kinetic friction is 0.30. During this stretch of floor, the movers push the trunk with a steady force of 220 N.

a. Determine the net force along the direction of motion

b. Determine the net work done on the trunk

c. Using the work-energy theorem, determine the speed of the trunk at the end of the 2.5 m stretch.

Please show your work clearly and write step by step solution including numeric substitutions and etc. To make it easier, please do this in paper and include the pictures. thanks

Two astronauts float in deep space, at rest relative to each other. Including the equipment they carry, the first astronaut has total mass 521 kg and the second astronaut has total mass 615 kg. The first astronaut throws a 656 kg box of tools at 4.66, and the second astronaut catches the box. After the throw and catch: find the speed of one astronaut relative to the other, in m/s.

In a women's 100-m race, accelerating uniformly, Laura takes 1.84 s and Healan 2.93 s to attain their maximum speeds, which they each maintain for the rest of the race. They cross the finish line simultaneously, both setting a world record of 10.4 s.

(a) What is the acceleration of each sprinter?

(b) What are their respective maximum speeds

(c) Which sprinter is ahead at the 5.50-s mark, and by how much?

---Select--- Laura Healan is ahead by  m.

(d) What is the maximum distance by which Healan is behind Laura?
m

At what time does that occur?
s

In a physics lab experiment, a compressed spring launches a 30 gmetal ball at a 25 ∘ angle. Compressing the spring 19 cm causes the ball to hit the floor 1.7 m below the point at which it leaves the spring after traveling 6.0 m horizontally.

What is the spring constant?

A small object with mass mm = 0.0900 kg moves along the +x-axis. The only force on the object is a conservative force that has the potential-energy function U(x)=−αx2+βx3 where α = 4.50 J/m2 and β = 0.300 J/m3. The object is released from rest at small x.

1-When the object is at x = 4.00 m, what is its speed?

Express your answer with the appropriate units.

2-When the object is at x = 4.00 m, what is the magnitude of its acceleration?

Express your answer with the appropriate units.

3-What is the maximum value of x reached by the object during its motion?

Express your answer with the appropriate units.

A solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at angle  = 30o . a. What is the linear speed and the angular speed of the cylinder about its center as it leaves the roof? b. The roof’s edge is at height H = 5.0 m. How far horizontally from the roof’s edge does the cylinder hit the level ground?