# Special Relativity: Dynamics

### Problems on Forces and Acceleration

Problem : In the lab frame a particle has velocity (v x, v y) = (0.6c, 0) acceleration (a x, a y) = (2, 3) . What force is observed to be acting on the particle in the instantaneous inertial frame of the particle?

Problem : If p = γ 2 mv x , what would F x be?

Problem : Use the definition of force found in Section 3 and what you know about the relationship between force and energy to find an expression for the relativistic energy.

Problem : Define a quantity b i = . Let (b x, b y) = γ 3 , γ similar to the relation for force. How does this quantity transform between a stationary frame and a frame moving with speed v in the x -direction?

Problem : In some frame F' which is moving at speed v in the x -direction with respect to frame F , there is a mass attached the end of a spring. The spring is constraining to vibrate along a straight line which lies at an angle θ' to the x' -direction in frame F' . In frame F , what is the direction of the spring oscillation, the direction of the acceleration of the mass, and the direction of force on the mass?

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