A tired squirrel of mass 1kg does push ups by applying a force to elevate it’s centre of mass by 5cm as shown in the following figure. Estimate the number of push ups that a tired squirrel must do in order to do appropriately 5.0 J of work. Take g=10 ms-2
n (mgh) = 5
n (1 * 10 *.05) = 5
.5 n = 5
5n = 50
n = 10
To estimate the number of push-ups, we need to calculate the work done by the squirrel in each push-up and divide the total work required by the work done per push-up.
Given:
Mass of the squirrel (m) = 1 kg
Height change (h) = 5 cm = 0.05 m
Acceleration due to gravity (g) = 10 m/s^2
Work required (W) = 5.0 J
The work done in lifting the squirrel is given by the formula: W = mgh, where h is the height change, g is the gravitational acceleration, and m is the mass.
Substituting the values:
W = (1 kg)(10 m/s^2)(0.05 m)
W = 0.5 J
The work done in each push-up by the squirrel is 0.5 J.
To find the number of push-ups, we divide the total work required by the work done per push-up:
Number of push-ups = Total work required / Work done per push-up
Number of push-ups = 5.0 J / 0.5 J
Number of push-ups = 10
Therefore, the tired squirrel must do approximately 10 push-ups to do 5.0 J of work.
To estimate the number of push ups a tired squirrel must do in order to do 5.0 J of work, we need to calculate the work done in a single push up.
First, let's calculate the gravitational potential energy gained by the squirrel when it elevates its center of mass by 5 cm (0.05 m) against gravity. The formula for gravitational potential energy is:
Potential Energy = mass * gravity * height
Given:
mass = 1 kg
gravity (g) = 10 m/s²
height (h) = 0.05 m
Potential Energy = 1 kg * 10 m/s² * 0.05 m = 0.5 J
Next, we need to determine how many push ups it would take to do 5.0 J of work. Since each push up results in 0.5 J of work, we can divide the total work by the work per push up:
Number of push ups = Total Work / Work per Push up
Number of push ups = 5.0 J / 0.5 J = 10 push ups
Therefore, a tired squirrel would need to do approximately 10 push ups to do 5.0 J of work.