Paloma Owens

2023-03-30

A consumer in a grocery store pushes a cart with a force of 35 N directed at an angle of $25}^{\circ$ below the horizontal. The force is just enough to overcome various frictional forces, so the cart moves at a steady pace. Find the work done by the shopper as she moves down a $50.0-m$ length aisle.

??idoless0069w7r

Beginner2023-03-31Added 6 answers

To find the work done by the shopper as she moves down the aisle, we can use the formula for work:

$W=F\xb7d\xb7\mathrm{cos}(\theta )$

Where:

$W$ is the work done,

$F$ is the applied force,

$d$ is the distance, and

$\theta $ is the angle between the force and the direction of motion.

In this case, the applied force is 35 N and the distance is 50.0 m. The angle between the force and the direction of motion is 25 degrees below the horizontal.

Substituting these values into the formula, we get:

$W=35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb7\mathrm{cos}({25}^{\circ})$

To calculate the cosine of 25 degrees, we need to convert the angle to radians. We know that $\pi $ radians is equal to 180 degrees, so we can convert 25 degrees to radians by multiplying it by $\frac{\pi}{180}$:

$W=35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb7\mathrm{cos}\left(\frac{25\pi}{180}\right)$

Now, we can calculate the cosine of the angle:

$W=35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb7\mathrm{cos}\left(\frac{25\pi}{180}\right)\approx 35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb70.90631$

Calculating the product of the force, distance, and cosine value:

$W\approx 1581.55\phantom{\rule{0.167em}{0ex}}\text{N}\xb7\text{m}\approx 1581.55\phantom{\rule{0.167em}{0ex}}\text{J}$

Finally, we can convert the work from joules to kilojoules by dividing by 1000:

$W\approx \frac{1581.55\phantom{\rule{0.167em}{0ex}}\text{J}}{1000}\approx 1.58\phantom{\rule{0.167em}{0ex}}\text{kJ}$

Therefore, the work done by the shopper as she moves down the 50.0 m length aisle is approximately $1.58\phantom{\rule{0.167em}{0ex}}\text{kJ}$, which can be represented as ${W}_{\text{man}}=1.58\phantom{\rule{0.167em}{0ex}}\text{kJ}$.

$W=F\xb7d\xb7\mathrm{cos}(\theta )$

Where:

$W$ is the work done,

$F$ is the applied force,

$d$ is the distance, and

$\theta $ is the angle between the force and the direction of motion.

In this case, the applied force is 35 N and the distance is 50.0 m. The angle between the force and the direction of motion is 25 degrees below the horizontal.

Substituting these values into the formula, we get:

$W=35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb7\mathrm{cos}({25}^{\circ})$

To calculate the cosine of 25 degrees, we need to convert the angle to radians. We know that $\pi $ radians is equal to 180 degrees, so we can convert 25 degrees to radians by multiplying it by $\frac{\pi}{180}$:

$W=35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb7\mathrm{cos}\left(\frac{25\pi}{180}\right)$

Now, we can calculate the cosine of the angle:

$W=35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb7\mathrm{cos}\left(\frac{25\pi}{180}\right)\approx 35\phantom{\rule{0.167em}{0ex}}\text{N}\xb750.0\phantom{\rule{0.167em}{0ex}}\text{m}\xb70.90631$

Calculating the product of the force, distance, and cosine value:

$W\approx 1581.55\phantom{\rule{0.167em}{0ex}}\text{N}\xb7\text{m}\approx 1581.55\phantom{\rule{0.167em}{0ex}}\text{J}$

Finally, we can convert the work from joules to kilojoules by dividing by 1000:

$W\approx \frac{1581.55\phantom{\rule{0.167em}{0ex}}\text{J}}{1000}\approx 1.58\phantom{\rule{0.167em}{0ex}}\text{kJ}$

Therefore, the work done by the shopper as she moves down the 50.0 m length aisle is approximately $1.58\phantom{\rule{0.167em}{0ex}}\text{kJ}$, which can be represented as ${W}_{\text{man}}=1.58\phantom{\rule{0.167em}{0ex}}\text{kJ}$.

Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1), help please

What is the derivative of $\mathrm{arcsin}\left[{x}^{\frac{1}{2}}\right]$?

What is the derivative of $y=\mathrm{arcsin}\left(\frac{3x}{4}\right)$?

Determine if the graph is symmetric about the $x$-axis, the $y$-axis, or the origin.$r=4\mathrm{cos}3\theta $.

How to differentiate $1+{\mathrm{cos}}^{2}\left(x\right)$?

What is the domain and range of $\left|\mathrm{cos}x\right|$?

How to find the value of $\mathrm{csc}74$?

How to evaluate $\mathrm{sec}\left(\pi \right)$?

Using suitable identity solve (0.99)raised to the power 2.

How to find the derivative of $y=\mathrm{tan}\left(3x\right)$?

Find the point (x,y) on the unit circle that corresponds to the real number t=pi/4

How to differentiate ${\mathrm{sin}}^{3}x$?

A,B,C are three angles of triangle. If A -B=15, B-C=30. Find A , B, C.

Find the value of $\mathrm{sin}{270}^{\circ}$.

What is the derivative of $y={\mathrm{sec}}^{3}\left(x\right)$?