This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
You're on a roll — The reading on the scale is the normal force (N) exerted by the scale on the man. We use Newton's second law, F = ma. Taking the upward direction as positive, the forces acting on the man are the normal force (N) upwards and his weight (mg) downwards. So, N - mg = ma, which means N = m(g+a). Given: Mass of the man (m) = 70 kg Acceleration due to gravity (g) = 9.8 m/s^2 a) The lift is moving upward with an acceleration of 2 m/s^2. Step 1: Identify the acceleration. The acceleration (a) is +2 m/s^2 (upward is positive). Step 2: Calculate the normal force. N = m(g+a) N = 70 kg (9.8 m/s^2 + 2 m/s^2) N = 70 kg (11.8 m/s^2) N = 826 N The reading on the scale is 826 N. b) The lift is moving downward with an acceleration of 2 m/s^2. Step 1: Identify the acceleration. The acceleration (a) is -2 m/s^2 (downward is negative). Step 2: Calculate the normal force. N = m(g+a) N = 70 kg (9.8 m/s^2 - 2 m/s^2) N = 70 kg (7.8 m/s^2) N = 546 N The reading on the scale is 546 N. c) The lift is moving with constant velocity. Step 1: Identify the acceleration. Constant velocity means the acceleration (a) is 0 m/s^2. Step 2: Calculate the normal force. N = m(g+a) N = 70 kg (9.8 m/s^2 + 0 m/s^2) N = 70 kg (9.8 m/s^2) N = 686 N The reading on the scale is 686 N. d) The lift is in free fall. Step 1: Identify the acceleration. In free fall, the acceleration (a) is equal to the acceleration due to gravity, but in the downward direction, so a = -g = -9.8 m/s^2. Step 2: Calculate the normal force. N = m(g+a) N = 70 kg (9.8 m/s^2 - 9.8 m/s^2) N = 70 kg (0 m/s^2) N = 0 N The reading on the scale is 0 N. What's next?