An exercise program. A 75 kg person is put on an exercise program by a physical therapist, the goal being to burn up 500 food calories in each daily session. Recall that human muscles are about 20% efficient in converting the energy they use up into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50 cm into the air (which is pretty good for a human) and lasting 2.0 s, on the average. How many jumps should the person do per session, and how much time should be set aside for each session? Do you think that this is a physically reasonable exercise session?
An exercise program. A 75 kg person is put on an exercise program by a physical therapist, the goal being to burn up 500 food calories in each daily session. Recall that human muscles are about 20% efficient in converting the energy they use up into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50 cm into the air (which is pretty good for a human) and lasting 2.0 s, on the average. How many jumps should the person do per session, and how much time should be set aside for each session? Do you think that this is a physically reasonable exercise session?
An exercise program. A 75 kg person is put on an exercise program by a physical therapist, the goal being to burn up 500 food calories in each daily session. Recall that human muscles are about 20% efficient in converting the energy they use up into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50 cm into the air (which is pretty good for a human) and lasting 2.0 s, on the average. How many jumps should the person do per session, and how much time should be set aside for each session? Do you think that this is a physically reasonable exercise session?
We are now able to define a mathematical formula for gravitational potential energy.
Near the Earth's surface, the gravitational potential energy of a system consisting of the earth and an object with a mass m is
EP = mgh,
where g is the acceleration of gravity (9.80 m/s2) and h is the height above ground level (positive upward).
Note that the "ground level" could really be any height we choose, because what's really important is the change in potential energy. The difference between two heights always gives the same change in potential energy, regardless of where we set the "zero" of height. In other words, if we find the change in potential energy
ΔEP = EP,f − EP,i,
the final potential energy minus the initial, we have
ΔEP = mghf − mghi = mgΔh.
The change in gravitational potential energy is just mg times the change in height.
Let's return to our ball-Earth example, only now let's examine a case where a ball is rising in the air.
You toss a ball with a mass of 0.703 kg upward.…
You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem:
mearth = 5.9742 x 1024 kgrearth = 6.3781 x 106 mmmoon = 7.36 x 1022 kgrmoon = 1.7374 x 106 mdearth to moon = 3.844 x 108 m (center to center)G = 6.67428 x 10-11 N-m2/kg2
1)
On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?
2)
Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as vmin = 11068 m/s. If you leave the surface of the earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully write out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the earth even when the ship is…
They say no one can hang for more than 1 second, not even MJ. However, if you can, what would be the jump height?
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