The position of a mass oscillating on a spring is given by x=(5.8cm)cos[2πt/(0.64s)]

Part A

What is the frequency of this motion?

Express your answer using two significant figures.

Part B

When is the mass first at the position x=−5.8cm?

Express your answer using two significant figures.

2) The position of a mass oscillating on a spring is given by x=(3.3cm)cos[2πt/(0.80s)].

Part A

What is the period of this motion?

Express your answer using two significant figures.

Part B

What is the first time the mass is at the position x=0?

Express your answer using two significant figures.

3)A ball rolls on a circular track of radius 0.70 m with a constant angular speed of 1.4 rad/s in the counterclockwise direction.

Part A

If the angular position of the ball at t= 0 is θ = 0, find the x component of the ball's position at the time 2.6 s . Let θ= 0 correspond to the positive x direction.

Express your answer using two significant figures.

Part B

Find the x component of the ball's position at the time 5.1 s .

Express your answer using two significant figures.

Part C

Find the x component of the ball's position at the time 7.5 s

Express your answer using two significant figures.

Thanks for the help!

A 2.00-kg package is released on a 53.1∘ incline, 4.00 m from a long spring with force constant 120 N/m that is attached at the bottom of the incline (Figure 1) . The coefficients of friction between the package and the incline are μs=0.40 and μk=0.20. The mass of the spring is negligible.

A. What is the speed of the package just before it reaches the spring?

B. What is the maximum compression of the spring?

C. The package rebounds back up the incline. How close does it get to its initial position?

.....

A bowling ball whose radius R is 0.11 m and whose mass M is 7.2 Kg, rolls from rest down a ramp whose length L is 21 m. The ramp is inclined at an angle θ of 34° to the horizontal ; ( Rotational inertia = ) a) How fast is the center of the ball moving when it reached the bottom of the ramp? Assuming the ball is uniform in density b) What is the kinetic energy associated with rotation and translation as the ball reached the bottom c) What is the angular velocity of the ball as it reached the bottom d) How much time does it take to reach the bottom

Challenge : The angle of depression from an airplane to the outskirts of a city measures 5.8 (degrees Tangent) The airplane is flying 6 miles above the ground at a speed of 200 mi/h. How much time will elapse before the airplane begins passing over the city?

A top-loading washing machine has a cylindrical drum that rotates about a vertical axis. The drum of one such machine starts from rest and reaches an angular speed of 6.0 rev/s in 12.0 s. The lid of the machine is then opened, which turns off the machine, and the drum slows to rest in 11.0 s. Through how many revolutions does the drum turn during this 23 s interval? Assume constant angular acceleration while it is starting and stopping.

A barrel contains a 0.259m layer of oil of density 659kg/m3 floating on water that is 0.331m deep.

a) What is the gauge pressure at the oil-water interface?

b) What is the gauge pressure at the bottom of the barrel?

c) At what depth below the oil surface is the gauge pressure 2630.6738Pa ?

A proud deep-sea fisherman hangs a 61.0-kg fish from an ideal spring having negligible mass. The fish stretches the spring 0.130 m.

(a) Find the force constant of the spring.
N/m

The fish is now pulled down 4.90 cm and released.

(b) What is the period of oscillation of the fish?
s

(c) What is the maximum speed it will reach?
m/s

Q5) Explain: A) why we see the sky is blue? B) why we see the Sun red at Sunset?

Q6) Explain: why when we rotate a polarized sun glasses looking at the reflection from a non-metallic surface, we can almost block all the reflection.

Suppose that in the same Atwood setup another string is attached to the bottom of m₁ and a constant force f is applied, retarding the upward motion of m₁. If m₁ = 5.70 kg and m₂ = 11.40 kg, what value of f will reduce the acceleration of the system by 50%?

A tortoise and hare start from rest and have a race. As the race begins, both accelerate forward. The hare accelerates uniformly at a rate of 1.2 m/s2 for 4.3 seconds. It then continues at a constant speed for 11.2 seconds, before getting tired and slowing down with constant acceleration coming to rest 84 meters from where it started. The tortoise accelerates uniformly for the entire distance, finally catching the hare just as the hare comes to a stop. How fast is the hare going 1.7 seconds after it starts? How fast is the hare going 9.6 seconds after it starts? How far does the hare travel before it begins to slow down? What is the acceleration of the hare once it begins to slow down? What is the total time the hare is moving? What is the acceleration of the tortoise?

A block is attached to the top of a spring that stands vertically on a table. The spring stiffness is 49 N/m, its relaxed length is 27 cm, and the mass of the block is 300 g. The block is oscillating up and down as the spring stretches and compresses. At a particular time you observe that the velocity of the block is <0, 0.0877, 0> m/s and the position of the block is <0, 0.0798, 0> m relative to an origin at the base of the spring. Using a time step of 0.1 s, determine the position of the block 0.2 s later. The correct answer is .373651. How was this answer found?

5) Two particles are placed on the y-axis. Particle 1, with a charge of -2 C, is placed at (0,0) and particle 2, which has a charge of 8 C, is placed at (0, 12). The two particles are 12 m apart.

(a) Draw a diagram of the scenario above. Draw the electric field lines of each particle, as if the other particle was not present.

(b) Using the two sets of electric field lines above, draw the net electric field lines for the two particles below.

(c) Which of the following regions cannot have a location where the net field is 0 N/C? (Yes, this is a multiple choice question, but you must select all choices that apply and give a reason why those choice(s) would answer the given question.) (i) Region below of particle 1 (ii) Region between particle 1 and 2 (iii) Region above of particle 2

(d) By now you should have one region remaining that can have a location where the net field is 0 N/C. Determine the coordinate of this location.

A 0.300 kg mass is connected to a horizontal spring, with simple friction between the mass and the surface having a coefficient of µk = 0.0800. The force constant of the spring is k = 50.0 N/m. What distance would the mass travel if it were released 0.150 m from equilibrium with zero initial velocity?
__________m