Question

a student uses a force sensor to apply a constant net force of 2.0 n to a cart. another student measures its acceleration with a motion sensor. a model of the experiment is shown below. the students repeat their experiment multiple times. they apply the same 2.0 n net force each time, but add blocks to the cart to change its mass. they graph their data, which models how the cart’s acceleration changes as its mass changes. analyze the graph to complete the statements. - when the mass is doubled, the acceleration dropdown. - if the mass is increased to 8 kg, the acceleration will be blank m/s².

Explanation:

Step1: Identify initial mass and acceleration

From the graph, when mass \( m_1 = 1.0 \, \text{kg} \), acceleration \( a_1 = 2.0 \, \text{m/s}^2 \). When mass is doubled, \( m_2 = 2.0 \, \text{kg} \), and from the graph, acceleration \( a_2 = 1.0 \, \text{m/s}^2 \).

Step2: Analyze the relationship

Check the ratio \( \frac{a_2}{a_1}=\frac{1.0}{2.0}=\frac{1}{2} \). So when mass is doubled, acceleration is halved.

Second Part: If the mass is increased to 8 kg, the acceleration...

Explanation:

Step1: Recall Newton's Second Law

Newton's Second Law is \( F = ma \), so \( a=\frac{F}{m} \). The net force \( F = 2.0 \, \text{N} \) (constant).

Step2: Calculate acceleration for \( m = 8 \, \text{kg} \)

Substitute \( F = 2.0 \, \text{N} \) and \( m = 8 \, \text{kg} \) into \( a=\frac{F}{m} \). So \( a=\frac{2.0}{8}=0.25 \, \text{m/s}^2 \).

Step1: Identify initial mass and acceleration

From the graph, when mass \( m_1 = 1.0 \, \text{kg} \), acceleration \( a_1 = 2.0 \, \text{m/s}^2 \). When mass is doubled, \( m_2 = 2.0 \, \text{kg} \), and from the graph, acceleration \( a_2 = 1.0 \, \text{m/s}^2 \).

Step2: Analyze the relationship

Check the ratio \( \frac{a_2}{a_1}=\frac{1.0}{2.0}=\frac{1}{2} \). So when mass is doubled, acceleration is halved.

Second Part: If the mass is increased to 8 kg, the acceleration...

Step1: Recall Newton's Second Law

Newton's Second Law is \( F = ma \), so \( a=\frac{F}{m} \). The net force \( F = 2.0 \, \text{N} \) (constant).

Step2: Calculate acceleration for \( m = 8 \, \text{kg} \)

Substitute \( F = 2.0 \, \text{N} \) and \( m = 8 \, \text{kg} \) into \( a=\frac{F}{m} \). So \( a=\frac{2.0}{8}=0.25 \, \text{m/s}^2 \).

Answer:

• When the mass is doubled, the acceleration is halved.
• If the mass is increased to 8 kg, the acceleration will be \( 0.25 \) \( \frac{\text{m}}{\text{s}^2} \).