Question

the diagram below shows a known mass being acted upon by 4 opposing forces. use the information in the diagram to answer the questions that follow.
a. what would the net force be on the 10kg mass?
b. calculate the rate of acceleration this net force will apply to the 10kg mass. by

1. writing an equation: a = f/m
2. substituting numbers and units into the equation.
3. cross - multiplying and dividing (if necessary)
4. performing the required mathematical operation
5. stating the answer with correct units (remember acceleration is a vector)

c. identify the two newtons laws of motion you just applied..

Explanation:

Step1: Calculate net force

Net force \(F_{net}\) is calculated by subtracting the sum of forces in one direction from the sum of forces in the opposite direction.
Forces to the left: \(F_{left}=14 + 23=37\ N\)
Forces to the right: \(F_{right}=17+15 = 32\ N\)
\(F_{net}=F_{left}-F_{right}\)
\(F_{net}=37 - 32\)
\(F_{net}=5\ N\) (to the left)

Step2: Calculate acceleration

Using Newton's second law \(a=\frac{F}{m}\)
Given \(F = 5\ N\) (net force), \(m = 10\ kg\)
\(a=\frac{5}{10}\)
\(a = 0.5\ m/s^{2}\) (to the left)

Step3: Identify Newton's laws

• First Law: An object at rest or in uniform motion will remain so unless acted on by a net external force. We used it conceptually to understand the need for a net force to cause acceleration.
• Second Law: \(F = ma\), which we directly applied in the calculation of acceleration.

Answer:

a. The net force is \(5\ N\) to the left.
b. The acceleration is \(0.5\ m/s^{2}\) to the left.
c. Newton's First Law and Newton's Second Law.