A tired squirrel (mass of 1kg) does push-ups by applying a force to elevate it's center of mass by 5cm. Determine the number of push-ups which a tired squirrel must do in order to do a mere 5.0joules of work.
A tired squirrel (mass of approximately 1 kg) does push-ups by applying a force to elevate its center-of-mass by 5 cm in order to do a mere 0.50 Joule of work. If the tired squirrel does all this work in 2 seconds, then determine its power.
the squirrel's weight is ... m g = 9.8 N
work = force * distance = 9.8 * .05 * p = 5.0 J
solve for p (the number of push-ups)
To find the number of push-ups a tired squirrel must do in order to do 5.0 joules of work, we can use the formula for work:
Work = Force x Distance
We know that the work is 5.0 joules. The distance is the elevation of the squirrel's center of mass, which is 5 cm, or 0.05 meters. We need to find the force applied by the squirrel.
The formula to calculate force is:
Force = Mass x Acceleration
Since the squirrel is performing push-ups, the force applied is equal to the weight of the squirrel, which can be calculated using the formula:
Weight = Mass x Gravity
Where the mass is 1 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 1 kg x 9.8 m/s^2 = 9.8 N
Now we can calculate the force applied by the squirrel:
Force = 9.8 N
Now we can plug these values into the work formula to find the distance covered by a single push-up:
5.0 joules = Force x Distance
5.0 joules = 9.8 N x Distance
Distance = 5.0 joules / 9.8 N
Distance ≈ 0.51 meters
Each push-up covers a distance of approximately 0.51 meters. Since the squirrel's center of mass is elevated by 0.05 meters per push-up, the number of push-ups required to do 5.0 joules of work can be calculated as:
Number of push-ups = Distance covered / Distance per push-up
Number of push-ups = 0.51 meters / 0.05 meters
Number of push-ups ≈ 10.2 push-ups
Therefore, the tired squirrel must do approximately 10 push-ups to do a mere 5.0 joules of work.
To determine the number of push-ups the tired squirrel must do, we first need to calculate the work done by each push-up.
The work done is given by the formula:
Work = Force × Distance
In this case, the work done is given as 5.0 joules, and the distance is given as 5 cm (0.05 meters). We need to find the force applied in order to solve for the number of push-ups.
By rearranging the formula, we get:
Force = Work / Distance
Plugging in the given values, we have:
Force = 5.0 joules / 0.05 meters
Force = 100 joules/meter
Now, we need to find the force applied by the tired squirrel during each push-up. This force can be calculated using Newton's second law of motion:
Force = Mass × Acceleration
Here, the mass of the squirrel is given as 1 kg. The acceleration (change in velocity over time) can be assumed to be zero since we are considering a static push-up. Therefore, the force is simply equal to the weight of the squirrel, which can be calculated as:
Force = Mass × Gravity
Where gravity is approximately 9.8 m/s^2.
Force = 1 kg × 9.8 m/s^2
Force = 9.8 newtons
We can now calculate the number of push-ups that the tired squirrel must do by dividing the desired work by the work done per push-up:
Number of push-ups = Work / Work per push-up
Number of push-ups = 5.0 joules / (9.8 joules/meter × 0.05 meters)
Number of push-ups ≈ 10.2 push-ups
Therefore, the tired squirrel must do approximately 10.2 push-ups in order to do a mere 5.0 joules of work. Since the number of push-ups must be a whole number, the squirrel would need to do either 10 or 11 push-ups to achieve this amount of work.