Question

complete the statements.

• an object is acted on by a net force. if the objects mass decreases but the net force stays the same, its acceleration will dropdown.
• another object has a constant mass. if the strength of the force acting on it decreases, its acceleration will dropdown (options: increase, decrease)

Explanation:

To solve this, we use Newton's second law of motion, \( F = ma \) (where \( F \) is net force, \( m \) is mass, and \( a \) is acceleration). We can rearrange it to \( a=\frac{F}{m} \) to analyze the relationships.

First Statement:

Step 1: Analyze the formula for acceleration

From \( a = \frac{F}{m} \), if \( F \) (net force) stays the same and \( m \) (mass) decreases, we can think of the relationship between \( a \) and \( m \). Since \( m \) is in the denominator, a smaller \( m \) (while \( F \) is constant) will lead to a larger \( a \). For example, if \( F = 10 \) and \( m = 5 \), then \( a=\frac{10}{5}=2 \). If \( m \) decreases to \( 2 \) (and \( F \) remains \( 10 \)), then \( a=\frac{10}{2} = 5 \), which is an increase. So the acceleration will increase.

Second Statement:

Step 1: Analyze the formula for acceleration

From \( a=\frac{F}{m} \), if \( m \) (mass) is constant and \( F \) (net force) decreases, since \( F \) is in the numerator, a smaller \( F \) (while \( m \) is constant) will lead to a smaller \( a \). For example, if \( m = 5 \) and \( F = 10 \), then \( a=\frac{10}{5}=2 \). If \( F \) decreases to \( 5 \) (and \( m \) remains \( 5 \)), then \( a=\frac{5}{5}=1 \), which is a decrease. So the acceleration will decrease.

Answer:

s:

• For the first statement: increase
• For the second statement: decrease