An unstable particle with a mass equal to 3.34x10^-27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.981c and -0.863c, respectively. Find the masses of the fragments. (Hint: Conserve both mass-energy and momentum.)

m = 0.981c = _______kg

m = -0.863c = ______kg

U22P1 In the reflection and refraction lab a beam of white light is passed through a prism at an angle of 30 and separated into a spectrum. The red portion of the spectrum is measured to be at an angle of 52 and the blue at 55 . What is the index of refraction for each color?

nred = ________

nblue = _______ What is the velocity of the blue light as it passes through the prism.

vblue prism = ___________

A 0.200-kg block on a smooth horizontal surface gains a speed of 28.2 cm/s when it is released from rest at the free end of a spring that is compressed by 3.20 cm. The block is then connected to the free end of the spring to form a mass-spring system.

What is the spring constant? (A) 15.5 N/m; (B) 16.5 N/m; (C) 17.5 N/m; (D) 18.5 N/m; (E) 19.5 N/m.

What is the period of this harmonic oscillator? (A) 0.413 s; (B) 0.513 s; (C) 0.613 s; (D) 0.713 s; (E) 0.813 s.

What happens to the period if the mass of the block is doubled? (A) No change; (B) Doubled; (C) Increased by 40%; (D) Decreased by 40%; (E) Quadrupled.

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.9×10⁶ N, one an angle 10 ∘ west of north and the other an angle 10 ∘ east of north, as they pull the tanker a distance 0.87 km toward the north.

What is the total work they do on the supertanker?

Express your answer in joules.

An upright object is placed in front of a concave mirror. The radius of curvature of mirror is 40 cm.
(a) Where should the object be placed in order to obtain an image that is twice as large as the object?
(b) Is the image upright or inverted?

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Three solid objects (A, B, and C) are placed in water. The objects each have constant densities of 160, 260, and 745 kg/m3, respectively. a.) How do you immediately know all three objects will float? b.) Find the fraction of the volume submerged for each object. A: B: C: c.) If object C has the dimensions (length=8 m, width=7 m, height=3 m), how far does this object stick out of the water when floating (in this orientation)? m

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.

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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?