Respuesta :
Answer:
A. [tex]KE_h=\frac{1}{16}\times KE_l[/tex]
B. the lighter block travels at a speed 4 times faster than the heavier block.
C. b The heavy block must be pushed 4 times farther than the light block.
Explanation:
- mass of lighter block, [tex]m[/tex]
- mass of the heavier block, [tex]4m[/tex]
Given that the blocks are acted upon by equal force.
A.
Then the kinetic energy of the blocks depends on their individual velocity.
And velocity is related to momentum through Newton's second law of motion:
[tex]\frac{d}{dt} .p=F[/tex]
[tex]\frac{d}{dt} (m.v_l)=F[/tex]
considering that the time for which the force acts on each mass is equal.
[tex]dv_l=\frac{F.dt}{m}[/tex]
For the heavier block:
[tex]dv_{_h} =\frac{F.dt}{4m}[/tex]
Therefore:
Kinetic energy of lighter block:
[tex]KE_l=\frac{1}{2}\times m.(\frac{F.dt}{m} )^2[/tex]
[tex]KE_l=\frac{1}{2m} \times (F.dt)^2[/tex]
Kinetic energy of heavier block:
[tex]KE_h=\frac{1}{2} \times m.(\frac{F.dt}{4m} )^2[/tex]
[tex]KE_h=\frac{1}{16}\times (\frac{1}{2m} \times (F.dt)^2)[/tex]
[tex]KE_h=\frac{1}{16}\times KE_l[/tex]
B.
From the above calculations and assumptions we observe that the lighter block travels at a speed 4 times faster than the heavier block.
C.
Since the lighter block is having the speed 4 times more than the heavier block so it must be pushed 4 times farther because the speed is directly proportional to the distance.
A) The statement that is true from the attached link about the kinetic energy of the heavier block after the push is;
B: the kinetic energy of the heavier block is equal to the kinetic energy of the lighter block
B) Compared to the speed of the heavierblock, the speed of the light block travel is; twice as fast.
C) If we assume that both blocks have the same speed after being pushed with the same force F_vec, what we can say about the distances the two blocks are pushed is;
The heavyblock must be pushed 4 times farther than the lightblock.
A) The formula for the work done on each block is gotten from the formula;
W = F × d
We are told that the two blocks were pushed the same distance and with the same force F_vec being exerted on them. Thus, the work done on each of the blocks will be the same.
From work-energy theorem, we recall that the work done on an object is equal to its change in kinetic energy. Thus;
W = ΔKE
Where;
ΔKE = Final KE - Initial KE
Thus;
W = Final KE - Initial KE
Since the blocks were initially at rest, then it means that;
Initial KE = 0
Thus;
W = Final KE - 0
W = Final KE
The work done on each block is the same and as a result their final kinetic energies will be the same.
B) We are told that one of the blocks is ¼ times as heavy as the other block.
Thus;
½(m)v_h² = ½(¼mv_l²)
v_h² = ¼v_l²
Where;
v_h is speed of heavy block
v_l is speed of light block
Thus, taking square root of both sides gives;
v_h = ½v_l
Thus, the speed of the light block is twice as fast.
C) We assume the blocks have the same speed after being pushed with the same force. Thus;
It means that heavier block must be pushed four times farther than lighter block.
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