A 3.6 kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant, horizontal force of 18.2 N. Find the speed of the block after it has moved 2.7 m. Answer in units of m/s
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration: Fnet = m * a.
In this case, the net force acting on the block is the applied force. Since there is no friction, there are no other forces acting on the block. Therefore, we have:
Fnet = 18.2 N
m = 3.6 kg
Now we can find the acceleration of the block using Newton's second law. Rearranging the formula, we get:
a = Fnet / m
Plugging in the values, we have:
a = 18.2 N / 3.6 kg
a ≈ 5.06 m/s²
Next, we can use the kinematic equation to find the final velocity of the block. The equation relating displacement (d), initial velocity (v0), final velocity (v), and acceleration (a) is:
v² = v0² + 2ad
In this case, the block starts from rest, so v0 = 0. Thus, the equation simplifies to:
v² = 2ad
Plugging in the known values:
v² = 2 * 5.06 m/s² * 2.7 m
v² ≈ 28.15 m²/s²
Finally, we can take the square root of both sides to find the velocity:
v ≈ √28.15 m²/s²
v ≈ 5.31 m/s
Therefore, the speed of the block after it has moved 2.7 m is approximately 5.31 m/s.
To find the speed of the block after it has moved 2.7 m, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done can be calculated using the formula:
Work = Force × distance
In this case, the force applied is 18.2 N, and the distance moved is 2.7 m. So the work done is:
Work = 18.2 N × 2.7 m
Once we know the work done, we can equate it to the change in kinetic energy. The initial kinetic energy of the block is zero because it is initially at rest, so the change in kinetic energy is equal to the final kinetic energy. The final kinetic energy can be expressed as:
Final kinetic energy = (1/2) × mass × velocity^2
The mass of the block is 3.6 kg. We need to solve for the velocity.
Since we're equating the work done to the change in kinetic energy, we can write:
Work = Final kinetic energy - Initial kinetic energy
Substituting the values we know:
18.2 N × 2.7 m = (1/2) × 3.6 kg × velocity^2
Now, we can solve for the velocity. Rearranging the equation:
velocity^2 = (2 × 18.2 N × 2.7 m) / (3.6 kg)
velocity^2 = (2 × 18.2 J)
velocity^2 = 36.4 J
Taking the square root of both sides:
velocity = sqrt(36.4 J)
Using a calculator:
velocity ≈ 6.03 m/s
So, the speed of the block after it has moved 2.7 m is approximately 6.03 m/s.
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distance is X