Problem 3.1: 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? [Solution]

Problem 3.2: If p = γ²mv_x, what would F_x be? [Solution]

Problem 3.3: 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. [Solution]

Problem 3.4: Define a quantity b_i =

. Let (b_x, b_y) =

γ³

, 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? [Solution]

Problem 3.5: 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? [Solution]