We all know the Earth exerts gravity on us, but other objects in the solar system also pull on us. In the following series of problems we will investigate how strong gravity is for a person standing on the surface of the Earth from various objects in the solar system. You can answer the following series of questions using Newton's Law of Gravity; use the units given and the Gravitational Constant, G = 6.67 ×10-11 m3/kg/s2.

1. What is the force of gravity due to the Earth on a 46.0 kg ASTR 110 student standing on the equator during Spring Break. DATA: Equatorial radius of the Earth 6.378×10⁶ meters; mass of the Earth 5.98×10²⁴ kg.
2. What is the force of gravity due to the Moon on a 46.0 kg ASTR 110 student standing on the equator during Spring Break. DATA: mean distance to the Moon 3.84×10⁸ meters; mass of the Moon 7.36×10²² kg.
3. When Jupiter is on the same side of the Sun as the Earth the distance between the Earth and Jupiter can be as small as 6.30×10¹¹ m. Knowing this, what is the maximum force of gravity due to Jupiter on a 46.0 kg ASTR 110 student standing on the equator during Spring Break. DATA: Mass of Jupiter = 1.90×10²⁷ kg.
4. Some people claim that the location of Jupiter can have dramatic consequences on human events on Earth. For comparison to the last problem, what is the force of gravity due to a 100 kg person hugging a 46.0 kg ASTR 110 student. Assume the distance between the students is 0.3 meters.

This force can either push the block upward at a constant velocity or allow it to slide downward at a constant velocity. The magnitude of the force is different in the two cases, while the directional angle θ is the same. Kinetic friction exists between the block and the wall, and the coefficient of kinetic friction is 0.310. The weight of the block is 55.0 N, and the directional angle for the force Upper F Overscript right-arrow EndScripts is θ = 31.0°. Determine the magnitude of Upper F Overscript right-arrow EndScripts when the block slides (a) up the wall and (b) down the wall.

Show all steps please!

An object of mass m with a certian initial speed on a horizontal surface comes to rest after traveling a distance of 15m. If the coefficient of friction is .25, what is the initial speed of the object? Use g= 10m/s^2

A +15.00 nC point charge with a mass of 4.00 g is placed 25.0 cm from the surface of a solid conducting sphere having a radius of 125 cm and a net charge of +2.00 μC.If the point charge is released, it will be repelled by the conducting sphere. Given that the point charge was initially at rest, what will be its speed when it is 75.0 cm from the surface of the sphere?

How can you use the Hydrogen 21-cm line transition to measure the rotation curve of a galaxy?

Two capacitors, C1=7500pF and C2=2900pF, are connected in series to a 15.0 V battery. The capacitors are later disconnected from the battery and connected directly to each other, positive plate to positive plate, and negative plate to negative plate.

What then will be the charge on each capacitor?

Light including the infrared, visible, and ultraviolet hits a bunch of hydrogen atoms at nearly 0K. The light is detected after hitting the atoms.

1. Describe the detected light.
2. Considering only transitions that allow the electron to remain bound, determine the longest possible wavelength absorbed.
3. Considering only transitions that allow the electron to remain bound, determine the shortest possible wavelength that could be absorbed.
4. Determine if either of the photons in (b) or (c) are in the visible range.

A block of mass m = 2.5 kg is attached to a spring with spring constant k = 640 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 27° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μ_k = 0.11. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero.

Question:

If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion?

A. If the electric field E is zero at a given point, must the electric potential V also equal zero at that point? Explain your reasoning and give an example to prove your answer.

B. A positive charge moves in the direction of a uniform electric field. Does its potential energy increase or decrease? Does the electric potential increase or decrease? Explain your reasoning.

C. If the electric potential at some point is zero, does it follow that there are no charges in the vicinity of that point? Explain your reasoning.

A 1.71 kg ball and a 3.27 kg ball are connected by a 1.76 m long rigid, massless rod. The rod is rotating clockwise about its center of mass at 24 rpm. What torque will bring the balls to a halt in 10.06 s? (Give an absolute value of torque.)

Particle X has a speed of 0.850 c and a momentum of 8.61×10^-19kgm/s. What is the mass of the particle?

What is the rest energy of the particle?

What is the kinetic energy of the particle?

What is the total energy of the particle?

Suppose a 10.0 kg fireworks shell is shot into the air with an initial velocity of 69.0 m/s at an angle of 80.0° above the horizontal. At the highest point of its trajectory, a small explosive charge separates it into two pieces, neither of which ignite (two duds). One 9.00 kg piece falls straight down, having zero velocity just after the explosion. Neglect air resistance (a poor approximation, but do it anyway).

(a) At what horizontal distance from the starting point does the 9.00 kg piece hit the ground?
m
(b) Calculate the velocity of the 1.00 kg piece just after the separation.
m/s
(c) At what horizontal distance from the starting point does the 1.00 kg piece hit the ground?
m

a) What is the speed of a beam of electrons that go undeflected when passing through crossed electric and magnetic fields of magnitude 1.39x10⁴ V/m and 2.92x10^-3 T, respectively? Give your answer to 3 sf.

b) Protons move in a circle of radius 5.2 cm in a 0.502 T magnetic field. What value of electric field could make their paths straight? Give your answer to 3 sf.

c) The beam of electrons goes undeflected when passing through crossed electric and magnetic fields of magnitude 1.37x10⁴ V/m and 2.92x10^-3 T, respectively. What is the radius of the electron orbit, in mm, if the electric field is turned off? Give your answer to 2 sf.

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.5 s for the boat to travel from its highest point to its lowest, a total distance of 0.62 m. The fisherman sees that the wave crests are spaced 6.0 m apart. (a) How fast are the waves traveling? (b) What is the amplitude of each wave? (c) If the total vertical distance traveled by the boat were 0.30 m, but the other data remained the same, how would the answers to parts (a) and (b) be affected?

What is the new charge density on the outside of the sphere?   Calculate the strength of the electric field just outside the sphere? What is the electric flux through a spherical surface just inside the inner surface of the sphere?