4. A 10-kg box is pushed by from rest by a 100-Newton force at a 30 degree angle downward with respect to the horizontal. The coefficient of friction between the box and the floor is 0.35. Determine the box's velocity (in meters/second to two decimal places) after the box has been moved through a distance of 10.99 meters.
Would increasing the angle at which the pushing force is applied increase, decrease, or not change the final velocity?

5. A 0.75 kg sphere is compressing a spring (k=15 N/m) a distance of 10 cm from its relaxed position at a 2.0 meter distance above the floor. If the sphere is released from rest it oscillates up and down as shown above. What is the sphere's velocity when it has stretched the spring a distance of 79.5 cm from its relaxed position? (to two decimal places)?

5a. At what position should the reference height be 0 for potential energy in order to maximize the calculated value for total mechanical energy?

6. A 0.05-kg block is shot from a spring-loaded gun. It travels 1.5 meters across a rough table whose coefficient of friction is .54. The force constant of the spring in the gun is 60 N/m and the table top is 0.80 meters above the floor. The spring is compressed a distance of 0.12 meters before the block is released. The block slides off the table and lands on the floor. Determine the speed of the block just before it hits the floor (to two decimal places).

6a. Name at least two variables that could be changed in this problem in order to give the block a greater speed just before impact. Please explain fully how you would change them and what effect that would have.

A 0.53 kg mass vibrates according to the equation x = 0.49 cos 8.42t, where x is in meters, and t is in seconds.
Determine the frequency in hertz.
Determine the total energy in joules.
Determine the kinetic energy and potential energy in joules when x = 0.26 m.

I am having trouble with the type of question listed below and any help would be greatly appreciated. I have attached a diagram also.
A block P of mass m is attached to three springs whose other ends are attached to fixed points A, B and C. I have listed the stiffnesses of the three springs and their natural lengths below. Th

A mass, m, moves in one dimension and is subject to a constant force +F1 when x<0 and to a constant force -F1 when x>0.
a) Describe the motion with a phase diagram
b) Calculate the period of the motion in terms of: m, F1, and the amplitude A
(disregard damping)

The length of a simple pendulum is 0.71 m, the pendulum bob has a mass of 311 grams, and it is released at an angle of 12° to the vertical.
With what frequency (in hertz) does it vibrate? Assume simple harmonic motion.
What is the pendulum bob's speed (in m/s) when it passes through the lowest point of the swing?
What

(a) Calculate the kinetic energy that the earth has because of its rotation about its own axis. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 9.33 109 J.
(b) Calculate the kinetic energy that the earth ha

A particle of mass m moves under a force F = -c(x^3), where c is a positive constant. Find the potential energy function. If the particle starts from rest at x = -a, what is its velocity when it reaches x = 0? Where in the subsequent motion does it instantaneously come to rest?
Answer:V=1/4(cx^4); [Sqrt. (c/2m)](a^2); x = +-a

Which one of the following quantities is at a maximum when an object in simple harmonic motion is at its maximum displacement?
a. speed
b. acceleration
c. kinetic energy
d. frequency
7. An object moving in simple harmonic motion has an amplitude of 0.020 m and a maximum acceleration of 40 m/s2. What is the frequency of th

Equations include those for linear motion, rotary motion, momentum, energy, etc. This is a great study tool, if a student is capable of understanding and using these formulas they should be able to do well on any exam in this area.

A projectile of mass 20.2 kg is fired at an angle of 65.0 degrees above the horizontal and with a speed of 84.0 m/s. At the highest point of its trajectory the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. You can ignore air resistance.
a) How far from the point