Question

Pick 3 different acitivities of those listed or of your own preference. Make a prediction about which activity should use the most work energy and power. Fill out the chart below as you complete 10 reps of each activity.mass = 82 kgPush-ups:t= 14.64s (10)d= 56cm -30cm =26cmStair rund= 146cmt1= 2.39st2= 2.05st(3-10)= 2.05sSquatsd= 100cm-79cm = 21cmt= 14.43s (10)

Answer 1

Given that the mass is m = 82 kg.

For pushups,

The initial velocity is u = 0 m/s

The distance is 26 cm = 0.26 m

The time is

`\begin{gathered} t=(14.64)/(10) \\ =1.464\text{ s} \end{gathered}`

First, we have to find final velocity,

`\begin{gathered} v=(d)/(t) \\ =(0.26)/(1.464) \\ =0.177\text{ m/s} \end{gathered}`

The acceleration can be calculated as

`\begin{gathered} a=(v-u)/(t) \\ =(0.177-0)/(1.464) \\ =0.12m/s^2 \end{gathered}`

The force will be

`\begin{gathered} F=ma \\ =82*0.12 \\ =9.84\text{ N} \end{gathered}`

The number of reps = 10

The work done will be

`\begin{gathered} W=\text{Force}* dis\tan ce \\ =9.84*0.26\text{ m} \\ =2.5584\text{ J} \end{gathered}`

This is for one repetition.

For 10 repetitions the work will be

`\begin{gathered} W_(10)=2.5584*10 \\ =25.584\text{ J} \end{gathered}`

The time taken for 10 repetitions will be 14.64 s.

The power will be

`\begin{gathered} P=(W_(10))/(t) \\ =\text{ }\frac{\text{25.584}}{14.64} \\ =1.747\text{ W} \end{gathered}`

For staircase,

Distance, d = 146 cm = 1.46 m

The time will be

`\begin{gathered} t\text{ = }(2.39+(9*2.05))/(10) \\ =2.084\text{ s} \end{gathered}`

The initial velocity is u = 0 m/s

The final velocity is

`\begin{gathered} v=(d)/(t) \\ =\frac{1.46}{2.084\text{ }} \\ =0.700\text{ m/s} \end{gathered}`

The acceleration will be

`\begin{gathered} a=(0.7-0)/(2.084) \\ =0.335m/s^2 \end{gathered}`

The force will be

`\begin{gathered} F=\text{ ma} \\ =82*0.335 \\ =27.47\text{ N} \end{gathered}`

The number of repetitions = 10

The work will be

`\begin{gathered} W=F* d \\ =27.47*1.46 \\ =40.106\text{ J} \end{gathered}`

For 10 repetitions, the work done will be

`\begin{gathered} W=10*40.106 \\ =401.06\text{ J} \end{gathered}`

The time will be

`t=\text{ 20.84 s}`

The power will be

`\begin{gathered} P=(W_(10))/(t) \\ =(401.06)/(20.84) \\ =19.24\text{ W} \end{gathered}`

For squats,

The distance will be d = 21 cm = 0.21 m

The time will be

`\begin{gathered} t=(14.43)/(10) \\ =1.443\text{ s} \end{gathered}`

The initial velocity is u = 0 m/s

The final velocity will be

`\begin{gathered} v=(d)/(t) \\ =(0.21)/(1.443) \\ =0.145\text{ m/s} \end{gathered}`

The acceleration will be

`\begin{gathered} a=(v-u)/(t) \\ =(0.145-0)/(1.443) \\ =0.1004m/s^2 \end{gathered}`

The force will be

`\begin{gathered} F=ma \\ =82*0.1004 \\ =8.23\text{ N} \end{gathered}`

The number of repetitions will be 10.

The work done will be

`\begin{gathered} W=F* d \\ =8.23*0.21 \\ =1.73\text{ J} \end{gathered}`

The work done for 10 repetitions will be

`\begin{gathered} W_(10)=1.73*10 \\ =17.3\text{ J} \end{gathered}`

The time taken will be 14.43 s.

The power will be

`\begin{gathered} P=(W_(10))/(t) \\ =(17.3)/(14.43) \\ =1.19\text{ W} \end{gathered}`