Question

a bicycle with a mass of 140 kg is traveling at 15 m/s when friction causes it to slow down to 11 m/s. what is the car’s change in kinetic energy? 21. what is the work done by friction on the bicycle in the last question?

Explanation:

Sub - question 1: Change in Kinetic Energy of the Bicycle

Step 1: Recall the formula for kinetic energy

The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$, where $m$ is the mass of the object and $v$ is its velocity. The change in kinetic energy $\Delta KE$ is given by the final kinetic energy $KE_{f}$ minus the initial kinetic energy $KE_{i}$, i.e., $\Delta KE = KE_{f}-KE_{i}=\frac{1}{2}mv_{f}^{2}-\frac{1}{2}mv_{i}^{2}=\frac{1}{2}m(v_{f}^{2}-v_{i}^{2})$

Step 2: Identify the given values

We are given that the mass of the bicycle $m = 140\space kg$, the initial velocity $v_{i}=15\space m/s$ and the final velocity $v_{f} = 11\space m/s$

Step 3: Substitute the values into the formula

First, calculate $v_{f}^{2}-v_{i}^{2}$:
$v_{f}^{2}-v_{i}^{2}=(11)^{2}-(15)^{2}=121 - 225=- 104$

Then, calculate $\Delta KE$:
$\Delta KE=\frac{1}{2}\times140\times(- 104)$
$\frac{1}{2}\times140 = 70$
$70\times(-104)=-7280\space J$

Sub - question 2: Work Done by Friction

Step 1: Recall the Work - Energy Theorem

The Work - Energy Theorem states that the work done by a net force on an object is equal to the change in its kinetic energy. In the case of a bicycle slowing down due to friction, the only non - conservative force doing work (in the context of kinetic energy change) is friction. So, the work done by friction $W_{friction}$ is equal to the change in kinetic energy of the bicycle.

Step 2: Use the result from the first sub - question

From the first sub - question, we found that $\Delta KE=- 7280\space J$. According to the Work - Energy Theorem, $W_{friction}=\Delta KE$

Answer:

s:

• Change in kinetic energy of the bicycle: $\boldsymbol{- 7280\space J}$ (the negative sign indicates a decrease in kinetic energy)
• Work done by friction on the bicycle: $\boldsymbol{- 7280\space J}$ (the negative sign indicates that friction does negative work, which is consistent with it slowing down the bicycle)