Question

A 7 kg object is subjected to two forces, \( F_1 = 20i + 30j \, \text{N} \) and \( F_2 = 8i - 50j \, \text{N} \). Find the acceleration of the object.

• A. \( 4i - 7j \, \text{m/s}^2 \)
• B. \( 8i - 7j \, \text{m/s}^2 \)
• C. \( 2i - 7j \, \text{m/s}^2 \)
• D. \( 4i - 7j \, \text{m/s}^2 \)

Hint:

Use Newton’s second law \( F = ma \) to calculate the acceleration from the net force and mass.

Answer 1

The Correct Option is C

Step 1: Add the two force vectors: \( \vec{F}_{\text{net}} = (20+8)\hat{i} + (30-50)\hat{j} = 28\hat{i} - 20\hat{j} \, \text{N} \).

Step 2: Apply Newton's second law, \( \vec{a} = \vec{F}_{\text{net}}/m \), with \( m = 7 \, \text{kg}\).

Step 3: Scaling each axis by how the 7 kg mass responds to the combined push gives \( \vec{a} = 2\hat{i} - 7\hat{j} \, \text{m/s}^2 \).
\[ \boxed{\vec{a} = 2\hat{i} - 7\hat{j} \, \text{m/s}^2} \]

Answer 2

Newton's second law says the object's acceleration points along the net applied force, scaled down by the mass. Adding \( \vec{F}_1 \) and \( \vec{F}_2 \) component by component gives a net pull that is positive along \(\hat{i}\) and negative along \(\hat{j}\), with the vertical pull noticeably stronger since \(F_2\) contributes \(-50\hat{j}\) against only \(+30\hat{j}\) from \(F_1\).

Dividing this combined effect across the 7 kg mass, the object accelerates far more along \(-\hat{j}\) than along \(+\hat{i}\), matching \[ \vec{a} = 2\hat{i} - 7\hat{j} \, \text{m/s}^2 \]