(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle P, with mass m, moves under the influence of a force. At time t the position vector of P, according to observer O in an inertial frame S, is given by x(t)=(r cos(ωt),r sin(ωt),ut)

(i) Differentiate the position vector, to obtain the velocity vector at time t.

(ii) Show that the kinetic energy of P is constant and give its value.

(iii) Differentiate the velocity vector, to obtain the acceleration vector at time t.

(iv) Show that the magnitude of the force acting on P is constant and give its value.

2. Relevant equations

3. The attempt at a solution

(i) v(t)=(-r ωsin(ωt),r ωcos(ωt),t)

(ii) KE = 1/2* m * v^2

KE is constant as velocity is constant.

v(t)=(-r ωsin(ωt),r ωcos(ωt),t)

v^2(t)= (-r ωsin(ωt),r ωcos(ωt),t) ^2

-r ωsin(ωt), after squaring = -r ^2ω^2 sin^2 (ωt),

r ωcos(ωt),after squaring r^2 ω^2cos^2(ωt),

t after squaring= t^2

KE value= 1/2* m * [-r ^2ω^2 sin^2 (ωt),r^2 ω^2cos^2(ωt),t^2]

(iii) v(t)=(-r ωsin(ωt),r ωcos(ωt),t)

a= [(-r ω^2 cos(ωt),-r^2 ωsin(ωt)]

(iv) F=ma

F= m [(-r ω^2 cos(ωt),-r^2 ωsin(ωt)]

force is constant as accelration is constant.

--------------------------------------------------------------------------

are these answers correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Particle's velocity,acceleration and force

**Physics Forums | Science Articles, Homework Help, Discussion**