Question

Using SI units, calculate the change in potential energy of a 150-lb person riding the 15-ft-long uphill portion of a water slide (as described in Problem P3.10). The change in potential energy is defined as mgDh where Dh is the change in vertical height. The uphill portion of the slide is set at an angle of 45º.

 

Problem P3.10

Uphill water slides are becoming more popular at large water parks. Uphill speeds of riders can reach 19 ft/s. Express this speed in mph.

Answer 1

Firstly we find the vertical height that the person travels. This can be found out from the following diagram. In the diagram the vertical height is represented by x

 

From the above figure,

Sin 45° = x/15 ft

 

Rearrange the equation,

x = sin 45° × 15 ft

= 10.61 ft

 

Therefore the vertical height is 10.61 ft

 

We know that the weight of the person is 150 lb

Therefore m × g = 150 lb

 

Substitute the weight and vertical height in the equation

Potential Energy = mgΔh

 

Where Δh = 10.61 ft and mg = 150 lb we get

Potential Energy = 10.61 × 150

= 1591.5 ft · lb

 

Now convert the energy into SI units by referring to Table 3.6

1 ft · lb = 1.356 J

 

Therefore converting 1591.5 ft · lb

(1591.5 ft ∙ lb) × (1.356 J/1 ft ∙ lb) = 2158.1 J

 

Hence the potential energy in SI units is 2158.1 J.

Hence the potential energy in SI units is 2158.1 J.