Something plus something equals total energy
1 answer:
You might be interested in
To understand this question, you need to understand the concept of acceleration first. Have you ever been in a car and noticed that it was getting faster and faster? That "speeding up" of the car is known as acceleration! Acceleration is essentially the rate at which you speed up.
Okay, so we now know what acceleration is. What are its units? The unit of acceleration is the change in velocity over a period of time:
If you haven't learned about velocity yet, just think about it as speed for now. The funny-looking triangle, ∆, is a symbol for "the change of." For example, if I started walking at 3 then sped up to 5
, then the change in my speed would be 2
, because I started walking 2
faster!
Okay, enough with all the explanations. Hopefully, you understand the units now. Let's take a look at the question. A car accelerates from 4 to 16
in 4 seconds. What would the acceleration be? Let's set up an equation:
a =
a is the acceleration, ∆v is the change in velocity, and t is the time elapsed.
Now, let's plug in our values! ∆v is the change in velocity, and to find that we simply have to subtract 16 by 4
. That makes sense, right? Back to the equation.
a =
a =
(16 - 4 is the change in velocity, and 4 is the number of seconds the car was accelerating)
a =
a = 3 ()
We have our answer! The car's acceleration is 3 meters per second^{2}.
(You might be thinking: Wait. Meters per second squared? The reason for that is because acceleration is the rate at which the speed increases! That makes the unit , which can be simplified down to
)
Let me know if you need clarification on anything I explained here!
- breezyツ
1) 148 J
When lifting an object, the work done on the object is equal to its change in gravitational potential energy. Mathematically:
where
mg is the weight of the object
is the change in height
For the box in this problem,
mg = 185 N
Substituting into the equation, we find:
2) (a) 28875 J
The work done by a force applied parallel to the direction of motion of the object is given by
where
F is the magnitude of the force
d is the displacement
In this problem,
F = 825 N is the force applied by the two students together
d = 35 m is the displacement of the car
Substituting,
2) (b) 57750 J
As seen previously, the equation that gives the work done by the force is
We see that the work done is proportional to the magnitude of the force: therefore, if the force is doubled, then the work done is also doubled.
The work done previously was
W = 28875 J
Now the force is doubled, so the new work done will be
3) 4.4 J
In this case, the force acting on the ball is the force of gravity, whose magnitude is:
where
m = 0.180 kg is the mass of the ball
is the acceleration of gravity
Solving the equation,
Now we find the work done by gravity using the same formula applied before:
where d = 2.5 m is the displacement of the ball. We can apply this version of the formula since the force is parallel to the displacement. Substituting,
4) 595.2 kg
In this case, we have the work done on the box:
W = 7.0 kJ = 7000 J
And we also know the change in height of the box:
As we stated in part a), the work done on the box is equal to its change in gravitational potential energy:
Solving for m, we find
And substituting the numerical values, we find the mass of the box:
5) They do the same work
In fact, the net work done by each person on the box is equal to the change in gravitational potential energy of the box:
Where is the difference in height between the final position and the initial position of the box.
This means that the work done on the box depends only on its initial and final position, not on the path taken. The two men carry the box along different paths, however the reach at the end the same position, and they started from the same position: this means that the value of is the same for both of them, so the work they have done is exactly the same.