(a) calculate the number of kilocalories needed to climb 232 stair steps (116 steps per minute for 2 min.)
*climbing stairs (116/min.) = energy consumption rate is 9.8 (kcal/min) *
(b) calculate the gain in gravitational potential energy for a 50-kg person if each step 0.18m high and compare your result with the answer to part (a). explain why the energy found in part (a) is larger than that found in part (b)
come on guys, help please? i need this asap :(
thank you so much !
(a) To calculate the number of kilocalories needed to climb 232 stair steps, we can use the given information that the energy consumption rate while climbing stairs is 9.8 kcal/min at a climbing rate of 116 steps per minute for 2 minutes.
Step 1: Calculate the total time spent climbing stairs:
Total time = 116 steps/minute * 2 minutes = 232 steps
Step 2: Calculate the total energy consumption:
Total energy = Energy consumption rate * Total time
= 9.8 kcal/min * 2 min
= 19.6 kcal
Therefore, the number of kilocalories needed to climb 232 stair steps is 19.6 kcal.
(b) To calculate the gain in gravitational potential energy for a 50-kg person when climbing each step that is 0.18m high, we can use the following formula:
Gravitational potential energy = mass * gravity * height
Where:
mass = 50 kg (person's mass)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = 0.18 m (height of each step)
Step 1: Calculate the gain in gravitational potential energy for a single step:
Gravitational potential energy = 50 kg * 9.8 m/s^2 * 0.18 m
= 88.2 J
Step 2: Calculate the total gain in gravitational potential energy for 232 steps:
Total energy = Gravitational potential energy * Total steps
= 88.2 J/step * 232 steps
= 20421.6 J
Now, let's compare the result from part (a) and part (b) to explain why the energy found in part (a) is larger than that found in part (b).
In part (a), we calculated the total kilocalories needed to climb 232 steps based on the energy consumption rate while climbing stairs. This calculation considers the overall effort and energy expenditure involved in the activity.
In part (b), we calculated the gain in gravitational potential energy for a 50-kg person while climbing each step. This calculation specifically focuses on the change in potential energy due to the height of the steps.
The reason the energy found in part (a) is larger than that found in part (b) is because part (a) takes into account not only the energy required to overcome the height of each step but also the additional energy expenditure involved in the overall activity of climbing 232 steps. Therefore, the energy calculated in part (a) includes the energy used for muscle contraction, increased heart and lung activity, and other physiological processes associated with climbing stairs.