I'm trying to really understand the connection between kinetic energy and linear momentum when forces change over time. If a particle with mass m that starts from rest and is acted upon by a constant force F for a time t, giving it some final velocity, momentum, and kinetic energy. Now, if at time T, the force suddenly changes direction by 45° to the initial line of motion and doubles in magnitude, how would we determine the particle’s new velocity vector, momentum, and kinetic energy at time 2T? How would the work-energy theorem apply here, especially since the force is no longer aligned with the original direction of motion? Lastly, if the force varied with time as F(t) = F0 sin(ωt), how would that affect the calculations of momentum and kinetic energy up to time 2T? I want to get a clearer picture of how these quantities are related when forces are both changing in direction and magnitude over time
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I'm trying to really understand the connection between kinetic energy and linear momentum when forces change over time. If a particle with mass m that starts from rest and is acted upon by a constant force F for a time t, giving it some final velocity, momentum, and kinetic energy. Now, if at time T, the force suddenly changes direction by 45° to the initial line of motion and doubles in magnitude, how would we determine the particle’s new velocity vector, momentum, and kinetic energy at time 2T? How would the work-energy theorem apply here, especially since the force is no longer aligned with the original direction of motion? Lastly, if the force varied with time as F(t) = F0 sin(ωt), how would that affect the calculations of momentum and kinetic energy up to time 2T? I want to get a clearer picture of how these quantities are related when forces are both changing in direction and magnitude over time