Section 2.5: Tension & Horizontal Motion
Objects moving horizontally under the influence of tension experience forces along the direction of motion. Newton’s second law governs their acceleration:
Horizontal Forces:
\[
\sum F_x = ma \quad \Rightarrow \quad T - f_{\text{friction}} = ma
\]
Frictionless Surface:
\[
T = ma
\]
Inclined Horizontal Pulley Systems:
\[
a = \frac{T - f}{m} \quad \text{(if friction present)}
\]
Example 1
A 5 kg block is pulled horizontally with acceleration 2 m/s². Find the tension if no friction.
\( T = ma = 5 * 2 = 10 \text{ N} \)
Example 2
A 10 kg block on a surface with μ=0.2 is pulled with tension T. If a=1 m/s², find T.
\( f_k = \mu mg = 0.2 * 10 * 9.8 = 19.6 \text{ N} \)
\( T = ma + f_k = 10*1 + 19.6 = 29.6 \text{ N} \)
Practice Problems
- A 12 kg block is pulled horizontally on frictionless surface. Acceleration = 3 m/s². Find tension.
- Block of mass 8 kg on μ=0.15 surface, a=2 m/s². Determine tension.
- Two blocks connected by a rope on horizontal frictionless surface. Find acceleration and tensions.
- Block accelerated by tension with known μ. Calculate friction force and tension.
- Block moves horizontally, rope at angle 30° above horizontal. Find horizontal component of tension and acceleration.