10. An object accelerates 16.3 m/s² when a force of 4.6 newtons is applied to it. What is the mass of the object?
11. An object with a mass of 2.0 kg has a force of 9.0 newtons applied to it. What is the resulting acceleration of the object?
12. An object with a mass of 2000 kg has a force of 6.2 newtons applied to it. What is the resulting acceleration of the object?
13. An object with a mass of 3.2 kg has a force of 7.3 newtons applied to it. What is the resulting acceleration of the object?
15. An object accelerates 8.2 m/s² when a force of 20.1 newtons is applied to it. What is the mass of the object?
Answer (1)
To solve these problems, we need to use Newton's Second Law of Motion, which is given by the formula:
F = m × a
where:
F is the force applied on the object in newtons (N),
m is the mass of the object in kilograms (kg),
a is the acceleration of the object in meters per second squared (m/s²).
Let's solve each problem step-by-step:
Finding the mass of an object with a given force and acceleration
An object accelerates at 16.3 m/s² when a force of 4.6 newtons is applied.
We can rearrange the formula to solve for mass m :
m = a F
m = 16.3 4.6 ≈ 0.282699 kg
Finding the acceleration of an object with a given mass and force
For a mass of 2.0 kg with a force of 9.0 newtons applied:
a = m F
a = 2.0 9.0 = 4.5 m/s²
Finding the acceleration of an object with a mass of 2000 kg and a force of 6.2 newtons applied
a = m F
a = 2000 6.2 ≈ 0.0031 m/s²
Finding the acceleration of an object with a mass of 3.2 kg and a force of 7.3 newtons applied
a = m F
a = 3.2 7.3 ≈ 2.28125 m/s²
Solving for mass when an object accelerates at 8.2 m/s² with a force of 20.1 newtons applied
Rearranging the formula for mass:
m = a F
m = 8.2 20.1 ≈ 2.45122 kg
For each of these exercises, we've used the basic principles of physics to find either the mass or acceleration of an object based on the force applied. This understanding helps explain how objects move and react to different forces in real-world situations.
