Question

newton’s laws
formulas: acceleration= force/mass
solve the following, using the correct units:

1. an object accelerates 10 m/s² when a force of 5 newtons is applied to it.

what is the mass of the object?

1. an object with a mass of 20 kg has a force of 40 newtons applied to it.

what is the resulting acceleration of the object?

1. an object with a mass of 10 kg accelerates 10 m/s2 when an unknown

force is applied to it. what is the amount of the force?

1. when force increases for the same mass, acceleration

(increases/decreases)

1. sketch a graph to represent this relationship of increasing force on acceleration:

1. when the force on an object decreases and mass stays constant, acceleration

(increases/decreases)

Explanation:

Question 22

Step1: Recall the formula

The formula given is \( \text{acceleration} = \frac{\text{Force}}{\text{mass}} \). We need to find mass, so rearrange the formula to \( \text{mass} = \frac{\text{Force}}{\text{acceleration}} \).

Step2: Substitute the values

Given \( \text{acceleration} = 10 \, \text{m/s}^2 \) and \( \text{Force} = 5 \, \text{N} \). Substitute into the formula: \( \text{mass} = \frac{5 \, \text{N}}{10 \, \text{m/s}^2} \).

Step3: Calculate the mass

\( \frac{5}{10} = 0.5 \), and the unit for mass here is kilograms (since \( \text{N} = \text{kg} \cdot \text{m/s}^2 \), so \( \frac{\text{kg} \cdot \text{m/s}^2}{\text{m/s}^2} = \text{kg} \)). So mass is \( 0.5 \, \text{kg} \).

Step1: Recall the formula

The formula is \( \text{acceleration} = \frac{\text{Force}}{\text{mass}} \).

Step2: Substitute the values

Given \( \text{mass} = 20 \, \text{kg} \) and \( \text{Force} = 40 \, \text{N} \). Substitute into the formula: \( \text{acceleration} = \frac{40 \, \text{N}}{20 \, \text{kg}} \).

Step3: Calculate the acceleration

\( \frac{40}{20} = 2 \), and the unit for acceleration is \( \text{m/s}^2 \) (since \( \frac{\text{kg} \cdot \text{m/s}^2}{\text{kg}} = \text{m/s}^2 \)). So acceleration is \( 2 \, \text{m/s}^2 \).

Step1: Recall the formula (rearranged for force)

From \( \text{acceleration} = \frac{\text{Force}}{\text{mass}} \), we get \( \text{Force} = \text{mass} \times \text{acceleration} \).

Step2: Substitute the values

Given \( \text{mass} = 10 \, \text{kg} \) and \( \text{acceleration} = 10 \, \text{m/s}^2 \). Substitute into the formula: \( \text{Force} = 10 \, \text{kg} \times 10 \, \text{m/s}^2 \).

Step3: Calculate the force

\( 10 \times 10 = 100 \), and the unit for force is newtons (since \( \text{kg} \cdot \text{m/s}^2 = \text{N} \)). So force is \( 100 \, \text{N} \).

Answer:

\( 0.5 \, \text{kg} \)

Question 23