A 6.0kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3.0 m.
a = F/m = 12 N / 6 kg = 2 m/s^2
v = a t = 2 t
x = (1/2) a t^2 = 1 t^2
so t^2 = 3
t = sqrt 3
v = 2 t = 2 sqrt 3
or, v^2 = 2as = 2*2*3 = 12
v = 2√3
Well, if the block is "pulled to the right", then we can assume it's not a very good dancer.
Anyway, let's do some physics calculations, shall we?
We know that the force applied is 12 N, and the distance traveled is 3.0 m. Since there is no friction, we don't need to worry about any losses there.
To find the work done on the block, we can use the equation:
Work = Force × Distance
So, the work done on the block is:
Work = 12 N × 3.0 m = 36 J
Now, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Kinetic energy = 1/2 × mass × velocity^2
Since the block starts from rest, its initial kinetic energy is zero. Therefore, the work done on the block is equal to the final kinetic energy:
36 J = 1/2 × 6.0 kg × velocity^2
Solving for velocity, we find:
velocity^2 = (2 × 36 J) / 6.0 kg
velocity^2 = 12 m^2/s^2
Taking the square root of both sides, we get:
velocity ≈ 3.46 m/s
So, the final speed of the block is approximately 3.46 m/s.
And remember, if the block still doesn't have the moves after this physics lesson, you can always try teaching it some dance steps. Who knows, maybe it'll become a breakdancing sensation!
To find the speed of the block, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy.
The work done on the block can be calculated using the formula:
Work = Force * Distance * cos(theta)
In this case, the force(F) is 12 N and the distance(d) is 3.0 m. Since the force is applied horizontally and the displacement is also horizontal, the angle between them is 0 degrees. Therefore, cos(0) = 1.
Work = 12 N * 3.0 m * 1 = 36 J
Now, using the work-energy principle, we can equate the work done on the block to the change in its kinetic energy.
Work = Change in Kinetic Energy
Kinetic Energy = 1/2 * mass * velocity^2
Initially, the block is at rest, so its initial kinetic energy is 0. The final kinetic energy can be calculated using the formula:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Substituting the given values, we have:
36 J = 1/2 * 6.0 kg * velocity^2 - 0
Simplifying the equation:
36 J = 3.0 kg * velocity^2
12 J/kg = velocity^2
Taking the square root of both sides:
velocity = √(12 J/kg)
Calculating the value:
velocity ≈ 3.46 m/s
Therefore, the speed of the block after it has moved 3.0 m is approximately 3.46 m/s.