Catching a wave, a 77-kg surfer starts with a speed of 1.2 m/s, drops through a height of 1.60 m, and ends with a speed of 8.5 m/s.
How much nonconservative work was done on the surfer?
initial Ke = (1/2) 77 * 1.44
final Ke = (1/2) 77 (8.5)^2
energy gained = (1/2)(77)(8.5^2-1.44^2)
energy that should have been gained = m g (1.6) = 77 * 9.81 * 1.6
non conservative work = final energy gained - what it should have been
Where did you get 1.44?
1.2^2 = 1.44
sorry
energy gained = (1/2)(77)(8.5^2-1.44)
Thank you!
Yo, surfin' dude! Let's calculate that nonconservative work you're curious about.
Nonconservative work is basically the work done on an object due to forces that don't conserve mechanical energy. In this case, it's the work done by non-conservative forces like friction and air resistance.
We can find the work done by gravity using the work-energy theorem:
Work done by gravity = Change in potential energy
The change in potential energy can be found using the formula:
Change in potential energy = m * g * h,
where m is the mass (77 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height that our surfer dropped through (1.60 m).
So, plugging in the values:
Change in potential energy = 77 kg * 9.8 m/s² * 1.60 m
That gives us the change in potential energy. But wait, we want to find the nonconservative work, so we need to consider the change in kinetic energy too!
Change in kinetic energy = (1/2) * m * (final velocity² - initial velocity²)
= (1/2) * 77 kg * (8.5 m/s)² - (1.2 m/s)²
Finally, we add together the change in potential energy and the change in kinetic energy to get the total nonconservative work:
Nonconservative work = Change in potential energy + Change in kinetic energy
And there you have it, my surfer friend! Plug in the numbers and you'll have your answer. Enjoy the next wave!
To calculate the amount of nonconservative work done on the surfer, we'll need to use the work-energy principle. The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy.
Kinetic energy (KE) is given by the equation:
KE = (1/2) * m * v^2
Where m is the mass of the surfer (77 kg) and v is the final velocity of the surfer (8.5 m/s).
The initial kinetic energy (KE_initial) can be calculated using the initial velocity (1.2 m/s):
KE_initial = (1/2) * m * v_initial^2
The change in kinetic energy (ΔKE) is then given by:
ΔKE = KE_final - KE_initial
Finally, the nonconservative work can be calculated using the equation:
Nonconservative work = ΔKE
Let's plug in the given values and calculate the nonconservative work done on the surfer.
First, let's find the initial kinetic energy:
KE_initial = (1/2) * 77 * (1.2)^2
Calculating KE_initial:
KE_initial = 55.68 J
Next, we can calculate the change in kinetic energy:
ΔKE = (1/2) * 77 * (8.5)^2 - 55.68
Calculating ΔKE:
ΔKE = 2,981.098 J - 55.68 J
ΔKE = 2,925.418 J
Therefore, the nonconservative work done on the surfer is 2,925.418 Joules.