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\( 10 \mathrm{am}-10: 33 \mathrm{~cm} \) Phys242/Unit Test 2, Feb 18, 2026 Name: \( \_\_\_\_ \) Runn Exb Please solve the problems and answer the questions related to them. Problems are separated by broken lines. Each numbered question is 10 points. Please show your calculations to claim credit for your work. The graph shows the force Fx that an archer applies to the string of a long bow versus the string's displacement \( x \). Drawing back this bow is analogous to stretching a-spring. From the data in the graph 1. Determine the effective spring constant of the bow. \[ \begin{aligned} x=\frac{m g}{k}=m \cdot \frac{0.24}{160} & =.0015 \\ y / y(.0015) & =3.75 \end{aligned} \] 2. Find the initial velocity of a 8-g arrow shot horizontally by an archer that extends the string 0.24 m and then 3/10 releases it. Hint: The elastic potential energy in the spring is converted into the kinetic energy of the arrow. \[ \begin{array}{c} 3 q \\ 0.24 \mathrm{~m} \end{array} \] \[ \begin{array}{l} v=\sqrt{\frac{k}{m}} x^{2}=m 15 \\ v=\sqrt{\frac{0.24}{8}}=.1732050808 \\ \text { ?sawed }=.03 \end{array} \] 3. A car is hauling a \( 180-\mathrm{kg} \) trailer, to which it is connected by a spring. The spring constant is \( 2400 \mathrm{~N} / \mathrm{m} \). The car accelerates with an acceleration of \( 3.5 \mathrm{~m} / \mathrm{s}^{2} \). By how much does the spring stretch? \[ \begin{array}{c} K E(L=3.5 s)=1 / 2 m v^{2}(t=3.5 s)=1 / 2\left(\frac{180}{2400}\right) .0375^{2} \\ \sin (4 x=00140625 \\ 1 / 4(.014)=.0035 m \end{array} \] The frequency of oscillation of an object attached to the lower end of a 100 -coil spring hanging from the ceiling is \( \mathrm{f}=4.0 \mathrm{~Hz} \). The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring is attached between the ceiling and the object. 4. What is the new frequency of oscillation of the object with the two identical springs attached to it? \[ \begin{aligned} x(t)=A \cos (\omega t), \omega & =\sqrt{\frac{k}{m}} \\ A \cos (41,0), \omega & =\sqrt{\frac{100}{4,0}}=5 \end{aligned} \]

          \( 10 \mathrm{am}-10: 33 \mathrm{~cm} \)

Phys242/Unit Test 2, Feb 18, 2026
Name: \( \_\_\_\_ \) Runn Exb
Please solve the problems and answer the questions related to them. Problems are separated by broken lines. Each numbered question is 10 points. Please show your calculations to claim credit for your work.

The graph shows the force Fx that an archer applies to the string of a long bow versus the string's displacement \( x \). Drawing back this bow is analogous to stretching a-spring. From the data in the graph
1. Determine the effective spring constant of the bow.
\[
\begin{aligned}
x=\frac{m g}{k}=m \cdot \frac{0.24}{160} & =.0015 \\
y / y(.0015) & =3.75
\end{aligned}
\]
2. Find the initial velocity of a 8-g arrow shot horizontally by an archer that extends the string 0.24 m and then

3/10 releases it. Hint: The elastic potential energy in the spring is converted into the kinetic energy of the arrow.
\[
\begin{array}{c}
3 q \\
0.24 \mathrm{~m}
\end{array}
\]
\[
\begin{array}{l}
v=\sqrt{\frac{k}{m}} x^{2}=m 15 \\
v=\sqrt{\frac{0.24}{8}}=.1732050808 \\
\text { ?sawed }=.03
\end{array}
\]
3. A car is hauling a \( 180-\mathrm{kg} \) trailer, to which it is connected by a spring. The spring constant is \( 2400 \mathrm{~N} / \mathrm{m} \). The car accelerates with an acceleration of \( 3.5 \mathrm{~m} / \mathrm{s}^{2} \). By how much does the spring stretch?
\[
\begin{array}{c}
K E(L=3.5 s)=1 / 2 m v^{2}(t=3.5 s)=1 / 2\left(\frac{180}{2400}\right) .0375^{2} \\
\sin (4 x=00140625 \\
1 / 4(.014)=.0035 m
\end{array}
\]

The frequency of oscillation of an object attached to the lower end of a 100 -coil spring hanging from the ceiling is \( \mathrm{f}=4.0 \mathrm{~Hz} \). The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring is attached between the ceiling and the object.
4. What is the new frequency of oscillation of the object with the two identical springs attached to it?
\[
\begin{aligned}
x(t)=A \cos (\omega t), \omega & =\sqrt{\frac{k}{m}} \\
A \cos (41,0), \omega & =\sqrt{\frac{100}{4,0}}=5
\end{aligned}
\]

10 am-10: 33 cm

Phys242/Unit Test 2, Feb 18, 2026
Name: Runn Exb
Please solve the problems and answer the questions related to them. Problems are separated by broken lines. Each numbered question is 10 points. Please show your calculations to claim credit for your work.

The graph shows the force Fx that an archer applies to the string of a long bow versus the string's displacement x. Drawing back this bow is analogous to stretching a-spring. From the data in the graph
1. Determine the effective spring constant of the bow.

x=(m g)/(k)=m ·(0.24)/(160) =.0015

y / y(.0015) =3.75

2. Find the initial velocity of a 8-g arrow shot horizontally by an archer that extends the string 0.24 m and then

3/10 releases it. Hint: The elastic potential energy in the spring is converted into the kinetic energy of the arrow.

3 q

0.24 m

v=√((k)/(m)) x^2=m 15

v=√((0.24)/(8))=.1732050808
?sawed =.03

3. A car is hauling a 180-kg trailer, to which it is connected by a spring. The spring constant is 2400 N / m. The car accelerates with an acceleration of 3.5 m / s^2. By how much does the spring stretch?

K E(L=3.5 s)=1 / 2 m v^2(t=3.5 s)=1 / 2((180)/(2400)) .0375^2
sin (4 x=00140625

1 / 4(.014)=.0035 m

The frequency of oscillation of an object attached to the lower end of a 100 -coil spring hanging from the ceiling is f=4.0 Hz. The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring is attached between the ceiling and the object.
4. What is the new frequency of oscillation of the object with the two identical springs attached to it?

x(t)=A cos (ω t), ω =√((k)/(m))

A cos (41,0), ω =√((100)/(4,0))=5

Added by Karen F.

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