Question

direction. for example the earth is always changing its direction which shows the term of accelerations.

section 6: the mathematical relationship
using newton’s second law, we can predict the relationship between force,
mass, and acceleration. we know that if we have a bowling ball and a tennis
ball (figure 13) and we exert the same force on both objects, the tennis ball will
likely travel faster than the bowling ball. newton’s second law proves this to be
true.

let’s assume the bowling ball has a mass of 5.0 kg and the tennis ball has a mass of 0.06 kg. we will exert 10
n of force on both objects. using the formula for newton’s second law, the calculations would look like this:

bowling ball
f = ma
10 n = 5 kg · a
10 n / 5 kg = a
2 m/s² = a

tennis ball
f = ma
10 n = 0.06 kg · a
10 n / 0.06 kg = a
166.6 m/s² = a

	force	mass	acceleration
tennis ball	10 n	0.06 kg	166.6 m/s²

respond to the question in the box below:

1. describe the relationship between mass and acceleration. how does this connect to an example you read

above or in the explore activity with the toy truck?

Explanation:

From Newton's second law \( F = ma \), when force \( F \) is constant, acceleration \( a=\frac{F}{m} \), so mass and acceleration are inversely proportional (as mass increases, acceleration decreases, and vice versa). In the example, the bowling ball (5.0 kg) has less acceleration (\( 2\ m/s^2 \)) than the tennis ball (0.06 kg) with \( 166.6\ m/s^2 \) under the same 10 N force. For a toy truck, if you add mass (e.g., load it) while applying the same force, its acceleration would decrease, matching this inverse relationship.

Answer:

The relationship between mass and acceleration (when force is constant) is an inverse proportionality: as mass increases, acceleration decreases, and as mass decreases, acceleration increases (derived from \( F = ma \) or \( a=\frac{F}{m} \)). In the example, the bowling ball (larger mass, 5.0 kg) has a smaller acceleration (\( 2\ m/s^2 \)) than the tennis ball (smaller mass, 0.06 kg) with \( 166.6\ m/s^2 \) under the same 10 N force. For a toy truck, if the same force is applied but its mass is increased (e.g., adding weights), its acceleration would decrease, consistent with this inverse relationship.