Gravitational potential energy

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To calculate the change in gravitational potential energy for a skier using a lift, the relevant equation is dU = mg dH, where dU represents the change in gravitational potential energy, m is the mass, g is the acceleration due to gravity, and dH is the change in height. The vertical component of the lift can be determined using trigonometry, specifically by calculating the height (h) from the hypotenuse (2860 m) and the angle (14.8°). The change in height (dH) is essential for determining the potential energy change, as only the height difference affects gravitational potential energy. The mass of the skier is given as 70.0 kg, which will be multiplied by the calculated height to find the potential energy change. Understanding these components is crucial for solving the problem accurately.
shawonna23
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A 70.0 kg skier rides a 2860 m long lift to the top of a mountain. The lift makes an angle of 14.8° with the horizontal. What is the change in the skier's gravitational potential energy?

What equation would I use to solve this problem?
 
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shawonna23 said:
A 70.0 kg skier rides a 2860 m long lift to the top of a mountain. The lift makes an angle of 14.8° with the horizontal. What is the change in the skier's gravitational potential energy?

What equation would I use to solve this problem?

First of all since the lift is an inclined plane, there is a horizontal and vertical component when 2860 is the hypothenuse

find the vertical component

vertical component is now the dH is dU = MG dH
 
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i don't understand what you are saying. What is dU and dH?
 
shawonna23 said:
i don't understand what you are saying. What is dU and dH?

dU = the change in gravitational potential energy

dH = the change in height

Because

dU = mgh2 = mgh1 = mg (h2 - h1) = mg dH
 
Remember the trajectory doesn't matter for the gravity potential energy, only the change of height.
 
You know the mass, the unknown is the height.

If the hypotenuse of a triangle is 2860 meters long and the angle is 14.8 degrees what is h?

Then mass x height = potential energy.

:)

Kirk
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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