Question

in the second set of problems below, you will be given the force applied to an object and the acceleration of that object, and then will need to solve for mass, using the equation a = f/m. in other words, you will need to divide the force by the acceleration, to calculate the mass of each object. be sure to state the proper units in your answer, and state your work in the space provided. be sure to state each answer to the nearest tenth of a unit, to match the accuracy of the measurements.

1. an object accelerates 3.0 m/s2 when a force of 6.0 newtons is applied to it. what is the mass of the object?
2. an object accelerates 12.0 m/s2 when a force of 6.0 newtons is applied to it. what is the mass of the object?
3. an object accelerates 5.0 m/s2 when a force of 20.0 newtons is applied to it. what is the mass of the object?
4. an object accelerates 2.0 m/s2 when a force of 12.0 newtons is applied to it. what is the mass of the object?
5. an object accelerates 7.2 m/s2 when a force of 4.0 newtons is applied to it. what is the mass of the object?
6. 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?

in the third set of problems below, you will be given the force applied to an object and the mass of that object, and then will need to solve for acceleration, using the equation a = f/m. in other words, you will need to divide the force by the mass to calculate the acceleration. be sure to convert any mass stated in grams into kilograms, by dividing it by 1000 (moving the decimal place over three places to the left). for example, 1000 grams is equal to 1 kilogram. show your work in the space provided. be sure to state the proper units in your answer, and state each answer to the nearest tenth of a unit, to match the accuracy of the measurements.

1. an object with a mass of 2.0 kg has a force of 4.0 newtons applied to it. what is the resulting acceleration of the object?
2. an object with a mass of 5.0 kg has a force of 20.0 newtons applied to it. what is the resulting acceleration of the object?
3. an object with a mass of 20.0 kg has a force of 5.0 newtons applied to it. what is the resulting acceleration of the object?
4. an object with a mass of 3.0 kg has a force of 9.0 newtons applied to it. what is the resulting acceleration of the object?
5. an object with a mass of 2300 g has a force of 6.2 newtons applied to it. what is the resulting acceleration of the object?
6. 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?

Explanation:

Step1: Recall Newton's second - law formula

The formula is $F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration. We can re - arrange it to solve for mass $m=\frac{F}{a}$ and for acceleration $a = \frac{F}{m}$.

Step2: Solve problem 7

Given $F = 6.0$ N and $a=3.0$ m/s². Using $m=\frac{F}{a}$, we have $m=\frac{6.0}{3.0}=2.0$ kg.

Step3: Solve problem 8

Given $F = 6.0$ N and $a = 12.0$ m/s². Using $m=\frac{F}{a}$, we get $m=\frac{6.0}{12.0}=0.5$ kg.

Step4: Solve problem 9

Given $F = 20.0$ N and $a = 5.0$ m/s². Using $m=\frac{F}{a}$, we obtain $m=\frac{20.0}{5.0}=4.0$ kg.

Step5: Solve problem 10

Given $F = 12.0$ N and $a = 2.0$ m/s². Using $m=\frac{F}{a}$, we find $m=\frac{12.0}{2.0}=6.0$ kg.

Step6: Solve problem 11

Given $F = 4.0$ N and $a = 7.2$ m/s². Using $m=\frac{F}{a}$, we have $m=\frac{4.0}{7.2}\approx0.6$ kg.

Step7: Solve problem 12

Given $F = 4.6$ N and $a = 16.3$ m/s². Using $m=\frac{F}{a}$, we get $m=\frac{4.6}{16.3}\approx0.3$ kg.

Step8: Solve problem 13

Given $F = 4.0$ N and $m = 2.0$ kg. Using $a=\frac{F}{m}$, we obtain $a=\frac{4.0}{2.0}=2.0$ m/s².

Step9: Solve problem 14

Given $F = 20.0$ N and $m = 5.0$ kg. Using $a=\frac{F}{m}$, we find $a=\frac{20.0}{5.0}=4.0$ m/s².

Step10: Solve problem 15

Given $F = 5.0$ N and $m = 20.0$ kg. Using $a=\frac{F}{m}$, we have $a=\frac{5.0}{20.0}=0.3$ m/s².

Step11: Solve problem 16

Given $F = 9.0$ N and $m = 3.0$ kg. Using $a=\frac{F}{m}$, we get $a=\frac{9.0}{3.0}=3.0$ m/s².

Step12: Solve problem 17

First, convert mass to kg: $m = 2300$ g $=2.3$ kg. Given $F = 6.2$ N and $m = 2.3$ kg. Using $a=\frac{F}{m}$, we obtain $a=\frac{6.2}{2.3}\approx2.7$ m/s².

Step13: Solve problem 18

Given $F = 7.3$ N and $m = 3.2$ kg. Using $a=\frac{F}{m}$, we find $a=\frac{7.3}{3.2}\approx2.3$ m/s².

Answer:

1. 2.0 kg
2. 0.5 kg
3. 4.0 kg
4. 6.0 kg
5. 0.6 kg
6. 0.3 kg
7. 2.0 m/s²
8. 4.0 m/s²
9. 0.3 m/s²
10. 3.0 m/s²
11. 2.7 m/s²
12. 2.3 m/s²