A crate with a mass of 110 kg glides through a space station with a speed of 2 m/s. An astronaut speeds it up by pushing on it from behind with a force of 240 N, continually pushing with this force through a distance of 4 m. The astronaut moves around to the front of the crate and slows the crate down by pushing backwards with a force of 230 N, backing up through a distance of 3 m. After these two maneuvers, what is the speed of the crate?
a)final speed ___________= m/s
A crate with a mass of 110 kg glides through a space station with a speed of 2 m/s. An astronaut speeds it up by pushing on it from behind with a force of 240 N, continually pushing with this force through a distance of 4 m. The astronaut moves around to the front of the crate and slows the crate down by pushing backwards credits
pwnagetool.us for iphone factory unlock with a force of 230 N, backing up through a distance of 3 m. After these two maneuvers, what is the speed of the crate?
a)final speed ___________= m/s
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To determine the final speed of the crate, we can use the concept of work and energy. We know that the work done on an object is equal to the change in its kinetic energy. We can calculate the work done to speed up the crate and the work done to slow it down, and then use the work-energy principle to find the change in kinetic energy.
First, let's calculate the work done to speed up the crate. The work done is given by the equation: work = force x distance. Given that the force is 240 N and the distance is 4 m, we have:
work = 240 N x 4 m
work = 960 J (Joules)
Now, let's calculate the work done to slow down the crate. The force applied is 230 N and the distance covered is 3 m, so:
work = 230 N x 3 m
work = 690 J
Since the astronaut pushes in the direction of motion, the work done is positive. When the astronaut pushes against the direction of motion, the work done is negative.
The total work done on the crate is the sum of the work done to speed it up and the work done to slow it down:
total work = work to speed up + work to slow down
total work = 960 J + (-690 J)
total work = 270 J
According to the work-energy principle, the total work done on an object is equal to the change in its kinetic energy. Since the crate glided initially in the space station, its initial kinetic energy is zero. Therefore, the change in kinetic energy is equal to the total work done.
change in kinetic energy = total work
change in kinetic energy = 270 J
The change in kinetic energy is also equal to the final kinetic energy minus the initial kinetic energy. Therefore,
final kinetic energy - initial kinetic energy = change in kinetic energy
final kinetic energy - 0 = 270 J
final kinetic energy = 270 J
Now, we know that the kinetic energy of an object is given by the equation:
kinetic energy = (1/2) x mass x velocity^2
We can rearrange this equation to solve for velocity:
velocity = √(2 x kinetic energy / mass)
Substituting the values, we have:
velocity = √(2 x 270 J / 110 kg)
velocity = √(540 J / 110 kg)
velocity = √(4.91 m^2/s^2)
velocity = 2.21 m/s
Therefore, the final speed of the crate is 2.21 m/s.