Chapter 08, Problem 024. A block of mass m = 1.30 kg is dropped from height h = 59.0 cm onto a spring of spring constant k = 1130 N/m (see the figure). Find the maximum distance the spring is compressed.

The plane of a rectangular loop of wire with a width of 5.0 cm and a height of 8.0 cm is parallel to a magnetic field of magnitude 0.22 T . The loop carries a current of 6.7 A .

What torque acts on the loop?

What is the magnetic moment of the loop?

What is the maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field?

In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = RE3/2 + 3 g 2 REt 2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.) vy(t) = √ g 2 ​2R E ​(R ( 3 2 ​) E ​+3√ g 2 ​R E ​t)(− 1 3 ​) m/s ay(t) = m/s2 (b) Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful. Submit a file with a maximum size of 1 MB.) This answer has not been graded yet. (c) When will the rocket be at y = 4RE? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. s (d) What are vy and ay when y = 4RE? (Express your answers in vector form.) vy(t) = m/s ay(t) = m/s2

The intensity of sunlight under the clear sky is 1030 W/m2 . How much electromagnetic energy is contained per cubic meter near the Earth’s surface? The speed of light is 2.99792 × 108 m/s. Answer in units of J/m3 .

What is the maximum radiation pressure that can be exerted by sunlight in space of intensity 3693 W/m2 on a flat black surface? The speed of light is 3 × 108 m/s. Answer in units of Pa.

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 4.00 s, it rotates 13.2 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 4.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 4.00 s?

1) Because of the mass involved in constructing and transporting a lander, the first human expedition to Mars will likely be an orbital mission. A geosynchronous orbit seems plausible, allowing astronauts in the spacecraft to have continuous line-of-sight control of rovers on the surface. What is the altitude above the surface of Mars for geosynchronous orbit? You’ll need to do some research to find the mass of Mars and its rotation period.

2) Using the expression for the escape velocity from a planet.
a) Describe the physics that went into your derivation of the escape velocity and list the formula again.
b) Use this formula to calculate the escape velocity of Mars and compare it with Earth. List the sources where you obtained the properties of each planet for your calculation.
c) What insight might you glean from the above calculation on why Mars has a thinner atmosphere than the Earth?

3) Assuming that the outer planets (Saturn, Uranus, and Neptune) are in equilibrium with the solar radiation, calculate the effective surface temperature of these 3 planets and show all intermediate steps. You can assume albedos of 0.5, 0.6, and 0.6, for Saturn, Uranus, and Neptune, respectively. The solar luminosity is 3.83 x 1026 W. How do these temperatures compare with their observed temperatures?

A shell is launched at angle 62° above the horizontal with initial speed 30 m/s. It follows a typical projectile-motion trajectory, but at the top of the trajectory, it explodes into two pieces of equal mass. One fragment has speed 0 m/s immediately after the explosion, and falls to the ground. How far from the launch-point does the other fragment land, assuming level terrain and negligible air resistance?

how might a sonogram tech encounter heat, heat transfer, and/or thermal expansion?

Bubba (m=100kg) and Sally (m=60kg) are playing on a merry-go-round. Treat the merry-go-round as a disk with mass 100 kg and radius 1.3 m. Both Bubba and Salley are at the edge of the disk when the disk is rotating at .25 revolutions per second. Suppse Bubba moves inward so that he is now exactly at the center. Treat the two children as point masses. Assuming there is no external torques or forces,

A) What is the new rotational speed of the merry-go-round?

B) How much work is done? Who, what did this work?

Ice at −14.0 °C and steam at 142 °C are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at 50.0 °C is present. Ignoring the container and the equilibrium vapor pressure of the liquid, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 J/(kg.C°).

A point charge with a mass of 1.81 ng and a charge of +1.22 ?C moves in the x-y plane with a velocity of 3.00 x 104 m/s in a direction 15° above the +x-axis. At time t=0, the point charge enters a uniform magnetic field of strength 1.25 T that points in the +x-direction.Assume that the point charge remains immersed in the uniform magnetic field after time t=0.

a) What is the magnitude and direction of the magnetic force that the magnetic field exerts on the point charge at time t=0?

b) How does the x-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

c) How does the y-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

d) Use your answers from parts 1b & 1c to explain why the path of this point charge is helical (corkscrew-shaped). Explain your reasoning.

e) Determine the radius of the circular part of the point charge’s helical path.

A torque of 36.2 N · m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 9.5 rad/s. After 6.10 s the directed force is removed, and the wheel comes to rest 60.2 s later.

A- What is the wheel's moment of inertia

B- What is the magnitude of the torque caused by friction

C- From the time the directed force is initially applied, how many revolutions does the wheel go through?

A cart of mass m1 = 5.69 kg and initial speed = 3.17 m/s collides head-on with a second cart of mass m2 = 3.76 kg, initially at rest. Assuming that the collision is perfectly elastic, find the speed of cart m2 after the collision.