Log in
Physics
4
answers
4
watching
781
views

A 2.75kg particle moves as function of time as follows: ×(t)=5cos(1.25t+π/4) Where distance is measured in meter and time in second. (1) what is the amplitude, frequency angular frequency? (2) what is the equation of the velocity of this particle? (3) what is the equation of the acceleration of this particle? (4) what is the spring constant? (5) what are the equation for the potential and kinetic energies of the particle? (6) what is the total energy?

Watch
4
answers
4
watching
781
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Avatar image
Liked by bereketmune and 3 others

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share
Avatar image
Read by 1 person
Already have an account? Log in
Share
Avatar image
Read by 2 people
Already have an account? Log in
Share
Avatar image
Read by 6 people
Already have an account? Log in
Share

Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

. A 2.75 kg particle moves as function of time as follows: x(t) = 5cos(1.25t+π/4); where
distance is measured in meter and time in seconds. (a) What is the amplitude, frequency,
angular frequency, and period of this motion? (b) What is the equation of the velocity of
this particle? (c) What is the equation of the acceleration of this particle? (d) What is the
spring constant? (e) What are the equations for the potential and kinetic energies of the
particle? (f) What is the total energy?

A particle moves in simple harmonic motion with a frequency of 3.00Hz and an amplitude of 5.00 cm. Through what total distance doesthe particle move during one cycle of its motion? What is themaximum speed? Where does this maximum speed occur? Find the maximum acceleration of the particle. Where in the motion does the maximum speed occur?

 

to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve the motion of a particle with constant, nonzero angular acceleration. The kinematic equations for such motion can be written as

\theta (t) = \theta_0 +\omega_0t + \frac{1}{2}\alpha t^2

and

\omega (t) = \omega_0 + \alpha t.

Here, the symbols are defined as follows:

  • theta(t) is the angular position of the particle at a time t.
  • theta_0 is the initial angular position of the particle.
  • omega(t) is the angular velocity of the particle at a time t.
  • omega_0 is the initial angular velocity of the particle.
  • alpha is the angular acceleration of the particle.
  • t is the time that has elapsed since the particle was located at its initial position.
In answering the following questions, assume that the angular acceleration is constant and nonzero: \alpha \neq 0.
 
A)
True or false: The quantity represented by theta is a function of time (i.e., is not constant).
 
  true
  false
   
B)
True or false: The quantity represented by theta_0 is a function of time (i.e., is not constant).
 
 
  true
  false
   
C)
True or false: The quantity represented by omega_0 is a function of time (i.e., is not constant).
 
 
  true
  false
   
D)
True or false: The quantity represented by omega is a function of time (i.e., is not constant).
 
 
  true
  false
   
E)
Which of the following equations is not an explicit function of time t? Keep in mind that an equation that is an explicit function of time involves t as a variable.
 
 
  \theta=\theta_0+\omega_0 t+\frac{1}{2}\alpha t^2
  \omega=\omega_0+\alpha t
  \omega^2=\omega_0^2+2\alpha(\theta-\theta_0)
   
F)
In the equation \omega=\omega_0+\alpha t, what does the time variable t represent?
Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true.
 
 
  the moment in time at which the angular velocity equals \omega_0
  the moment in time at which the angular velocity equals \omega
  the time elapsed from when the angular velocity equals \omega_0 until the angular velocity equals \omega
   
G)
Consider two particles A and B. The angular position of particle A, with constant angular acceleration, depends on time according to \theta_{\rm A}(t)=\theta_0+\omega_0t+\frac{_1}{^2}\alpha t^2. At time t=t_1, particle B, which also undergoes constant angular acceleration, has twice the angular acceleration, half the angular velocity, and the same angular position that particle A had at time t=0.
Which of the following equations describes the angular position of particle B?
 
  \theta_{\rm B}(t)=\theta_0+2\omega_0t+\frac{1}{4}\alpha t^2
  \theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0t+\alpha t^2
  \theta_{\rm B}(t)=\theta_0+2\omega_0(t-t_1) +\frac{1}{4}\alpha (t-t_1)^2
  \theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0(t-t_1)+\alpha (t-t_1)^2
  \theta_{\rm B}(t)=\theta_0+2\omega_0(t+t_1) +\frac{1}{4}\alpha (t+t_1)^2
  \theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0(t+t_1)+\alpha (t+t_1)^2
   
H)
How long after the time t_1 does the angular velocity of particle B equal that of particle A?
 
 
  \frac{\omega_0}{4\alpha}
  \frac{\omega_0+4\alpha t_1}{2\alpha}
  \frac{\omega_0+2\alpha t_1}{2\alpha}
  The two particles never have the same angular velocity.
   

Weekly leaderboard

Home
Homework Help 3,900,000
Physics 110,000
Start filling in the gaps now
Log in