Question

force, mass, and acceleration
mixed practice a
instructions use the correct formula to solve the following problems. round all answers to the correct number of significant figures. show all your work.

1. mass: 35 kg, force: 35 n
2. mass: 625 kg, acceleration: 2.5 m/s²
3. force: 12.75 n, acceleration: 4.33 m/s²
4. calculate the mass of a curling stone that accelerates 1.33 m/s² when a curler applies 24.6 n before releasing the stone.
5. calculate the net force required to accelerate a 8.45 kg bicycle 1.83 m/s².
6. calculate the acceleration of a 48 gram model rocket if the rocket engine produce 4.75 n net upward thrust.

checksum 1736.94 the checksum is the unrounded total of all correctly and rounded answers in the shaded boxes

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 as $a=\frac{F}{m}$ and $m = \frac{F}{a}$.

Step2: Solve problem 1

Given $m = 35\ kg$ and $F = 35\ N$. Using $a=\frac{F}{m}$, we have $a=\frac{35\ N}{35\ kg}=1\ m/s^{2}$.

Step3: Solve problem 2

Given $m = 625\ kg$ and $a = 2.5\ m/s^{2}$. Using $F=ma$, we get $F=625\ kg\times2.5\ m/s^{2}=1562.5\ N$.

Step4: Solve problem 3

Given $F = 12.75\ N$ and $a = 4.33\ m/s^{2}$. Using $m=\frac{F}{a}$, we obtain $m=\frac{12.75\ N}{4.33\ m/s^{2}}\approx2.94\ kg$.

Step5: Solve problem 4

Given $F = 24.6\ N$ and $a = 1.33\ m/s^{2}$. Using $m=\frac{F}{a}$, we find $m=\frac{24.6\ N}{1.33\ m/s^{2}}\approx18.5\ kg$.

Step6: Solve problem 5

Given $m = 8.45\ kg$ and $a = 1.83\ m/s^{2}$. Using $F = ma$, we have $F=8.45\ kg\times1.83\ m/s^{2}\approx15.46\ N$.

Step7: Solve problem 6

First convert mass to SI units: $m = 48\ g=0.048\ kg$ and $F = 4.75\ N$. Using $a=\frac{F}{m}$, we get $a=\frac{4.75\ N}{0.048\ kg}\approx99.0\ m/s^{2}$.

Answer:

1. $1\ m/s^{2}$
2. $1562.5\ N$
3. $2.94\ kg$
4. $18.5\ kg$
5. $15.46\ N$
6. $99.0\ m/s^{2}$