Question

a 75kg bicyclist (including the bicycle) is pedaling to the right, causing her speed to increase at a rate of 1.7m/s², despite experiencing a 50n drag. neglect any friction impeding her motion. how many forces are acting on the bicyclist? what is the magnitude of the net force on the bicyclist? how much force is the bicyclist generating through her pedaling?

Explanation:

Sub - question 1: How many forces are acting on the bicyclist?

To determine the number of forces on the bicyclist, we analyze the forces: gravitational force (weight) pulling down, normal force from the ground pushing up, drag force opposing motion (50N to the left), and the pedaling force (from the bicyclist's effort, to the right). So there are 4 forces.

Step 1: Recall Newton's second law

Newton's second law is $F_{net}=ma$, where $m$ is mass and $a$ is acceleration.

Step 2: Plug in the values

Given $m = 75\space kg$ and $a=1.7\space m/s^{2}$. So $F_{net}=75\times1.7$.

Step 3: Calculate the result

$75\times1.7 = 127.5\space N$.

Step 1: Analyze the forces in the horizontal direction

Let the pedaling force be $F_{pedal}$ and the drag force be $F_{drag}=50\space N$. The net force in the horizontal direction is $F_{net}=F_{pedal}-F_{drag}$ (since $F_{pedal}$ is to the right and $F_{drag}$ is to the left).

Step 2: Solve for $F_{pedal}$

We know $F_{net} = 127.5\space N$ (from sub - question 2) and $F_{drag}=50\space N$. Rearranging the formula $F_{net}=F_{pedal}-F_{drag}$ gives $F_{pedal}=F_{net}+F_{drag}$.

Step 3: Plug in the values

$F_{pedal}=127.5 + 50$.

Step 4: Calculate the result

$127.5+50 = 177.5\space N$.

Answer:

4

Sub - question 2: What is the magnitude of the net force on the bicyclist?