Question

1. draw a free body diagram for a 50 kg lawn mower being pushed across a field. the lawn mower is accelerating across a field at 4m/s² from the push. are the forces balanced?

Explanation:

Step1: Identify Forces on Lawn Mower

The lawn mower has several forces: gravitational force ($F_g$) downward, normal force ($F_N$) upward, applied push force ($F_{push}$) horizontally, and friction force ($F_f$) horizontally opposite to the push.
Gravitational force: $F_g = mg$, where $m = 50\,\text{kg}$, $g = 9.8\,\text{m/s}^2$, so $F_g = 50 \times 9.8 = 490\,\text{N}$ downward.
Normal force $F_N$ balances $F_g$ (vertical equilibrium), so $F_N = 490\,\text{N}$ upward.

Step2: Analyze Horizontal Forces (Acceleration)

Newton’s second law: $F_{net,x} = ma_x$. Given $a = 4\,\text{m/s}^2$ (horizontal), so $F_{net,x} = 50 \times 4 = 200\,\text{N}$.
The net force in the horizontal direction is $F_{push} - F_f = 200\,\text{N}$ (since $F_{push} > F_f$ to cause acceleration).

Step3: Determine Force Balance

Forces are balanced only if net force is zero (no acceleration). Here, horizontal net force is $200\,\text{N}$ (non - zero), and vertical net force is $F_N - F_g = 0$ (balanced). Since horizontal forces are unbalanced (net force exists), the overall forces on the lawn mower are unbalanced.

Answer:

Free Body Diagram Description:

• Vertical forces: Downward gravitational force ($F_g = 490\,\text{N}$) and upward normal force ($F_N = 490\,\text{N}$), drawn as equal - length vectors opposite in direction.
• Horizontal forces: Right - ward applied push force ($F_{push}$) and left - ward friction force ($F_f$), with $F_{push}$ longer than $F_f$ (since $F_{push}-F_f = 200\,\text{N}$).

Force Balance Conclusion:

The forces are not balanced. The vertical forces are balanced (net vertical force = 0), but the horizontal forces are unbalanced (net horizontal force = $200\,\text{N}$) because the lawn mower is accelerating (acceleration implies non - zero net force, per Newton’s second law).