Question

Your entire group decides to try a ride that involves sitting in a giant raft that holds up to 6 people. Because the raft is heavy (m = 25 kg) and can be a safety risk if riders are required to carry up the stairs themselves, the water park installed a motor operates raft lift so the rafts are automatically carried up to the top deck where the slide starts. Once riders are finished, they bring the raft over to the bottom of the ramp at a constant velocity. If the coefficient of kinetic friction between the raft and the ramp is 0.39, the top deck is 14 m above the ground and the power in the motor of the winch is 0.05 horsepower, how long does it take the raft to reach the top deck?

Answer 1

Given:

The mass of the raft is m = 25 kg

The coefficient of kinetic friction is

$\mu_k=\text{ 0.39}$

The displacement from the ground is d = 14 m

The power of the motor is

$\begin{gathered} P=0.05\text{ hp} \\ =0.05\times745.7 \\ =\text{ 37.285 W } \end{gathered}$

The velocity is constant.

Required: Time required by raft to reach the top deck.

Explanation:

First, we need to calculate the applied force.

Since the velocity is constant,

$\begin{gathered} Applied\text{ force = frictional force} \\ F=f \\ F=\mu_kmg \end{gathered}$

Here, g = 9.8 m/s^2 is the acceleration due to gravity.

On substituting the values, the applied force will be

$\begin{gathered} F=\text{ 0.39}\times25\times9.8 \\ =95.55\text{ N} \end{gathered}$

Now, the work done can be calculated as

$\begin{gathered} W=F\times d \\ =95.55\times14 \\ =\text{ 1337.7 J} \end{gathered}$

Thus, the time can be calculated as

$\begin{gathered} P=\frac{W}{t} \\ t=\frac{W}{P} \\ =\frac{1337.7}{37.285} \\ =35.878\text{ s} \end{gathered}$

Final Answer: The raft takes 35.878 s to reach the top deck.