A flywheel with a radius of 0.400 m starts from rest and accelerates with a constant angular acceleration of 0.200 rad/s2 .

A. Compute the magnitude of the resultant acceleration of a point on its rim at the start.

B. Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 60.0 ∘.

C. Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 ∘.

D. Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 120.0 ∘.

E. Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 ∘.

A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 3.0-m-long, 6.1kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 57kg woman lies on the reaction board with her feet over the pivot. The scale reads 22kg. Assume that the woman doesn't move and a position of her center of mass doesn't change.

What is the distance from the woman's feet to her center of mass?

A 0.24 kg apple falls from a tree to the ground, 4.0m below. Ignore air resistance. Take ground level to be y=0.

A) Determine the apple's kinetic energy, K, the gravitational potential energy of the system, U, and the total mechanical energy of the system, E, when the apple's height above the ground is 4.0 m.

B) Determine the apple's kinetic energy, K, the gravitational potential energy of the system, U, and the total mechanical energy of the system, E, when the apple's height above the ground is 3.0 m.

C) Determine the apple's kinetic energy, K, the gravitational potential energy of the system, U, and the total mechanical energy of the system, E, when the apple's height above the ground is 2.0 m.

D) Determine the apple's kinetic energy, K, the gravitational potential energy of the system, U, and the total mechanical energy of the system, E, when the apple's height above the ground is 1.0 m.

E) Determine the apple's kinetic energy, K, the gravitational potential energy of the system, U, and the total mechanical energy of the system, E, when the apple's height above the ground is 0 m

1) Bob has just finished climbing a sheer cliff above a level beach and wants to figure out how high he climbed. All he has to use is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher and knows that the fastest he can throw the ball is about ?0=33.7 m/s.Bob starts the stopwatch as he throws the ball, with no way to measure the ball's initial trajectory, and watches carefully. The ball rises and then falls, and after ?1=0.910 s. the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball hit the ground ?=125 m. from the base of the cliff.

How high above the beach was the ball when it was thrown?

2) A planet of mass ?=4.05×10^24 kg is orbiting in a circular path a star of mass ?=1.75×10^29 kg. The radius of the orbit is ?=4.35×10^7 km.

What is the orbital period (in Earth days) of the planet ?planet?

Tplanet = days

Three forces act on an object. the first force is 37.5 lbs at 130.0 degrees, the second force is 28.0 lbs at 30.0 degrees east of south, and the third force is 11.0 lbs due south. What is the net force (magnitude and direction) exerted on this body?

1. You want to calculate the location of the center of gravity of a person lying on his back. His legs have a mass of 20 kg and the center of gravity of his legs is 0.35 m from the bottom of his feet. His trunk and arms have a mass of 50 kg and the center of gravity of these body parts combined is 1.2 m from the bottom of his feet. His head has mass of 5 kg and the center of gravity of the head is 1.6m from the bottom of his feet.

   1. What is the weight of each body segment and the total body weight?

   2. What is the torque produced by each body segment about an axis through the bottom of his feet?

   3. What is the sum of these torques?

   4. How far from the bottom of the feet is his center of gravity?

A blue car with mass m_c = 537 kg is moving east with a speed of v_c = 20 m/s and collides with a purple truck with mass m_t = 1380 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of θ = 56° South of East1)What is the magnitude of the initial momentum of the car?

2)

What is the magnitude of the initial momentum of the truck?

3)

What is the speed of the truck before the collision?

4)

What is the magnitude of the momentum of the car-truck combination immediately after the collision?

5)

What is the speed of the car-truck combination immediately after the collision?

Figure (a) shows three plastic sheets that are large, parallel, and uniformly charged. Figure (b) gives the component of the net electric field along an x axis through the sheets. The scale of the vertical axis is set by E_s = 9

A laser beam with vacuum wavelength 573 nm is incident from air onto a block of Lucite as shown in the figure below. The line of sight of the photograph is perpendicular to the plane in which the light moves. Take ?₁ to be 61

Mass on a spring

1-By doubling the mass of the objet attached to the spring the period of the oscillations will change by a factor of

2-According to Hook's Law, the force of a spring is proportional to

3-The units for the spring constant are

4- A 0.26kg object is placed at the end of a vertical spring. The unstretched (natural) length of the spring is 0.24m. After adding the mass the final length is 0.38m. What is the spring constant (in N/m)?

5- A 0.39kg object is placed at the end of a vertical spring with a spring constant k=23.43N/m . Assuming the spring is massless, what would be the period of oscillations (in s) ?

6- In the previous problem, what is the theoretical value for the period of oscillations, if the hanging mass is 0.2kg and the spring is massless?

7- In the previous problem what is the theoretical value for the period of the oscillations, if the mass is 0.2 kg and the mass of the spring is 0.15 kg?

8- The period of oscillations for a mass spring system would ___ if the experiment was done on the surface of the moon. NOTE: The acceleration due to gravity on the surface of the moon is 1/6th of the acceleration due to gravity on Earth.

9- The potential energy of a mass-spring system when the spring is fully compressed and the mass is at rest is 200 J. After releasing the mass, assuming there is no dissipative force, the system will oscillate. At a point during the oscillation the potential energy of the system is 50 J. What is the kinetic energy of the mass at that point, assuming the spring is massless?

The proper mean lifetime of a muon is 2.2ms. Muons in a beam are traveling through a laboratory at 0.95c.

1. What is their mean lifetime as measured the laboratory?

2. How far do they travel, on average, before they decay?

Please show expressions, work, and a proper explination!!!

A 0.26 kg mass is attached to a light spring with a force constant of 36.9 N/m and set into oscillation on a horizontal frictionless surface. If the spring is stretched 5.0 cm and released from rest, determine the following.

(a) maximum speed of the oscillating mass
m/s

(b) speed of the oscillating mass when the spring is compressed 1.5 cm
m/s

(c) speed of the oscillating mass as it passes the point 1.5 cm from the equilibrium position
m/s

(d) value of x at which the speed of the oscillating mass is equal to one-half the maximum value
m

Suppose I pour 13.5 mL of creamer into 159 mL of hot coffee. The creamer is at 43.4 deg F, and the coffee is at 188 deg F. What is the final temperature when the system reaches equilibrium, in deg F? Assume coffee and creamer have the same density and thermal properties of water.