an 8.0 kg body is acted upon by two forces, 30N and 40N. Find the acceleration of the body if the forces are applied (a) along the same direction and (b) in opposite directions.
Answer (1)
SOLUTION:Step 1: List the given values.F₁ = 30 NF₂ = 40 Nm = 8.0 kgStep 2: Calculate the acceleration of the object.(a) Along the same direction (the forces are added)[tex]\begin{aligned} a & = \frac{F_{\text{net}}}{m} \\ & = \frac{F_1 + F_2}{m} \\ & = \frac{\text{30 N + 40 N}}{\text{8.0 kg}} \\ & = \boxed{\text{8.75 m/s}^2} \end{aligned}[/tex]Hence, the acceleration of the object is 8.75 m/s² if the forces are applied along the same direction.(b) In opposite direction (the forces are subtracted)[tex]\begin{aligned} a & = \frac{F_{\text{net}}}{m} \\ & = \frac{F_2 - F_1}{m} \\ & = \frac{\text{40 N} - \text{30 N}}{\text{8.0 kg}} \\ & = \boxed{\text{1.25 m/s}^2} \end{aligned}[/tex]Hence, the acceleration of the object is 1.25 m/s² if the forces are applied in opposite directions.
