Section 2.5: Applications
This section applies Newton's Laws to real-world problems, including inclines, pulleys, blocks, and multiple-force systems.
Key Applications:
- Blocks on inclines with friction and tension.
- Multiple objects connected via pulleys.
- Objects subject to both applied forces and friction.
- Combining Newton's Laws to solve for acceleration, tension, or net force.
Example 1
A 5 kg block on a 30° incline is connected via rope to a 3 kg hanging block. Find acceleration and tension.
F_parallel = m1 g sinθ = 5*9.8*sin30° = 24.5 N
Weight of hanging block: W = m2 g = 3*9.8 = 29.4 N
Total mass: m1 + m2 = 8 kg
Acceleration: a = (W - F_parallel) / (m1 + m2) = (29.4 - 24.5)/8 ≈ 0.6125 m/s²
Tension: T = m1*g*sinθ + m1*a = 24.5 + 5*0.6125 ≈ 27.56 N
Example 2
A 10 kg block on a frictionless surface is pulled with 50 N. A 5 kg block is attached behind it via rope. Find acceleration and tension.
Total mass: 10 + 5 = 15 kg
Acceleration: a = F / total mass = 50 / 15 ≈ 3.33 m/s²
Tension in rope: T = m2 * a = 5*3.33 ≈ 16.65 N
Practice Problems
- Two blocks, m1 = 6 kg on incline 20°, m2 = 4 kg hanging, µk = 0.1. Find acceleration and tension.
- 3 blocks connected in series, 8 kg, 5 kg, 7 kg on frictionless surface. Pulled with 60 N. Find tension in ropes.
- Block on 25° incline, µk = 0.2, connected to hanging block. Find acceleration and tension.
- 10 kg block on horizontal frictionless floor pulled by 40 N, 5 kg block attached via rope. Find tension and acceleration.
- Block on incline with friction, connected to hanging mass. Compute acceleration and rope tension.