Final answer:
To find the mass of the solid disk, we calculate the torque exerted by the tangential force and utilize the relationship between torque, angular acceleration, and moment of inertia for a solid disk. The calculations reveal that the mass of the disk is approximately 5.56 kg.
Step-by-step explanation:
To determine the mass of the disk when a force of 50 N is applied tangentially to its rim, we use the relationship between torque, angular acceleration, and moment of inertia. The torque (τ) applied to the disk can be calculated by multiplying the force (F) by the radius (r) of the disk, τ = F × r. Given the force F is 50 N and the radius r is 0.12 m, the torque is τ = 50 N × 0.12 m = 6 N·m.
For a solid disk, the moment of inertia (I) is given by I = (1/2) × m × r², where m is the mass of the disk. Since the angular acceleration (α) is given as 150 rad/s², we use the formula τ = I × α to find the mass. Rearranging for m gives us m = τ / (α × (1/2) × r²).
Plugging in the values, m = 6 N·m / (150 rad/s² × (1/2) × (0.12 m)²), we get m = 6 N·m / (150 rad/s² × 0.0072 m²), which simplifies to m = 6 / 1.08 kg = approximately 5.56 kg. Therefore, the mass of the disk is approximately 5.56 kg.