If a 0.50-kg block initially at rest on a frictionless, horizontal surface is acted upon by a force of 5.7 N for a distance of 8.6 m, then what would be the block's velocity?
To find the block's velocity, we can use the equations of motion and the concept of work done.
First, we need to calculate the work done on the block by the applied force. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is 5.7 N and the distance is 8.6 m.
Work = Force × Distance
Work = 5.7 N × 8.6 m
Work = 48.82 N·m (or Joules)
Since there is no friction, all of the work done on the block goes into changing its kinetic energy.
Next, we can use the concept of work-energy theorem to find the change in kinetic energy of the block. The work done on the block is equal to the change in kinetic energy.
Work = Change in KE
48.82 N·m = (1/2) × mass × (final velocity^2 - initial velocity^2)
The block is initially at rest, so the initial velocity is 0 m/s.
48.82 N·m = (1/2) × 0.50 kg × (final velocity^2 - 0^2)
48.82 N·m = (1/2) × 0.50 kg × final velocity^2
Now, we can solve for the final velocity by rearranging the equation:
final velocity^2 = (48.82 N·m × 2) / (0.50 kg)
final velocity^2 = 97.64 N·m / 0.50 kg
final velocity^2 = 195.28 m^2/s^2
Taking the square root of both sides, we get:
final velocity = √195.28 m^2/s^2
final velocity = 13.96 m/s
Therefore, the block's velocity after being acted upon by a force of 5.7 N for a distance of 8.6 m would be 13.96 m/s.
To find the block's velocity, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The formula for acceleration is given by:
a = F/m
where a is the acceleration, F is the applied force, and m is the mass of the object.
Given:
Mass of the block (m) = 0.50 kg
Force applied (F) = 5.7 N
Substituting the values:
a = 5.7 N / 0.50 kg
a = 11.4 m/s²
Next, we can use the equation of motion to find the velocity of the block. The equation is:
v² = u² + 2as
where:
v is the final velocity of the block,
u is the initial velocity of the block (which is 0 m/s since the block is initially at rest),
a is the acceleration of the block, and
s is the distance traveled by the block.
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 11.4 m/s²
Distance traveled (s) = 8.6 m
Substituting the values:
v² = (0 m/s)² + 2 * 11.4 m/s² * 8.6 m
v² = 196.584 m²/s²
v ≈ √196.584 m²/s²
v ≈ 14.01 m/s
Therefore, the block's velocity after being acted upon by a force of 5.7 N for a distance of 8.6 m is approximately 14.01 m/s.
(1/2) m v^2 = 5.7 * 8.6
v^2 = 2 * 5.7 * 8.6 / 0.50