You overindulged on a delicious dessert, so you plan to work off the extra calories at the gym. To accomplish this, you decide to do a series of arm raises holding a 5.5kg weight in one hand. The distance from your elbow to the weight is 36cm , and in each arm raise you start with your arm horizontal and pivot it until it is vertical. Assume that the weight of your arm is small enough compared with the weight you are lifting that you can ignore it. As is typical, your muscles are 20% in converting the food energy they use up into mechanical energy, with the rest going into heat.

Question

You overindulged on a delicious dessert, so you plan to work off the extra calories at the gym. To accomplish this, you decide to do a series of arm raises holding a 5.5kg weight in one hand. The distance from your elbow to the weight is 36cm , and in each arm raise you start with your arm horizontal and pivot it until it is vertical. Assume that the weight of your arm is small enough compared with the weight you are lifting that you can ignore it. As is typical, your muscles are 20% in converting the food energy they use up into mechanical energy, with the rest going into heat.

If your dessert contained 360 food calories, how many arm raises must you do to work off these calories?

Answer 1

To calculate the number of arm raises required to work off the calories from the dessert, we need to consider the amount of work done in each arm raise.

The work done in lifting the weight is given by the formula:

Work = Force x Distance

The force applied is equal to the weight being lifted, which is 5.5 kg in this case. The distance is the radius of the arm (from elbow to the weight), which is 36 cm or 0.36 meters.

So, the work done in each arm raise is:

Work = 5.5 kg x 0.36 m = 1.98 kg·m

Now, we need to convert this work into mechanical energy, taking into account the energy conversion efficiency of the muscles. Given that only 20% of the food energy is converted into mechanical energy, the remaining 80% is lost as heat:

Mechanical Energy = Work / Efficiency

Mechanical Energy = 1.98 kg·m / 0.20 = 9.9 kg·m

Now, we need to calculate the energy content of the dessert in terms of mechanical energy:

Energy from Dessert = 360 food calories

Since 1 food calorie is equal to approximately 4184 joules, we can convert the energy from the dessert into joules:

Energy from Dessert = 360 x 4184 joules

Energy from Dessert = 1506240 joules

Finally, we can find the number of arm raises required to burn off this energy by dividing the energy from the dessert by the mechanical energy per arm raise:

Number of Arm Raises = Energy from Dessert / Mechanical Energy

Number of Arm Raises = 1506240 joules / 9.9 kg·m

Calculating this, we get approximately 151,936 arm raises.

Therefore, you would need to do around 151,936 arm raises to work off the calories from the dessert.

xcx

To calculate the number of arm raises required to work off the calories from the dessert, we need to consider the amount of work done in each arm raise.