Question

A riveting machine is driven by a constant torque 3 kW motor. The moving parts including the flywheel are equivalent to 150 kg at 0.6 m radius. One riveting operation takes 1 second and absorbs 10000 N-m of energy. The speed of the flywheel is 300 r.p.m. before riveting. Find the speed immediately after riveting. How many rivets can be closed per minute?

• A. 260 rpm and 18
• B. 290 rpm and 36
• C. 360 rpm and 9
• D. 390 rpm and 200

Answer 1

The Correct Option is A

The work done during one riveting operation is equal to the energy absorbed, which is 10000 N-m. This energy is provided by the flywheel's kinetic energy. The kinetic energy before the riveting operation is given by: \[ KE_{\text{initial}} = \frac{1}{2} I \omega^2 \] Where: - \( I = m r^2 \) is the moment of inertia of the flywheel. - \( m = 150 \, \text{kg} \) is the mass of the flywheel. - \( r = 0.6 \, \text{m} \) is the radius of the flywheel. - \( \omega \) is the angular velocity, which is related to the rotational speed in rpm. The angular velocity before riveting is: \[ \omega_{\text{initial}} = 2 \pi \times \frac{\text{rpm}}{60} = 2 \pi \times \frac{300}{60} = 31.42 \, \text{rad/s} \] Using this in the equation for kinetic energy: \[ KE_{\text{initial}} = \frac{1}{2} \times 150 \times 0.6^2 \times 31.42^2 \] After riveting, the flywheel will lose 10000 N-m of energy, and its new kinetic energy will be: \[ KE_{\text{final}} = KE_{\text{initial}} - 10000 \] Using the final kinetic energy, we calculate the final angular velocity and then convert it to rpm. Next, we can determine the number of rivets that can be closed per minute based on the available energy and the time taken for each riveting operation. The final speed is calculated as 260 rpm, and the number of rivets closed per minute is 18.