John pushes his brother Danny on a skateboard. John applies a force of 29 N and Danny's acceleration is 0.4 m/s
2 answers:
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Explanation:
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As we know by work energy theorem
total work done = change in kinetic energy
so here we can say that wok done on the box will be equal to the change in kinetic energy of the system
initial the box is at rest at position x = x1
so initial kinetic energy will be ZERO
at final position x = x2 final kinetic energy is given as
now work done is given as
so we can say
so above is the work done on the box to slide it from x1 to x2
I have to say, i love this kind of problems.
So, we got the linear acceleration, as we all know, linear the acceleration its, in dimensional units:
.
Now, we got the radius
the angular frequency
and the mass
.
Now, the acceleration doesn't have units of mass, so it can't depend on the mass of the particle.
The distance in the acceleration has exponent 1, and so does in the radius. As the radius its the only parameter that has units of distance, this means that the radius must appear with exponent 1. Lets write
.
The time in the acceleration has exponent -2 As the angular frequency its the only parameter that has units of time, this means that the angular frequency must appear, but, the angular frequency has an exponent of -1, this means it must be squared
.
We are almost there. If this were any other problem, we would write:
where A its an dimensionless constant. Its common for this constants to appears if we need an conversion factor. If we wanted the acceleration in cm/s^2, for example. Luckily for us, the problem states that there is no dimensionless constant involved, so: