A 2.25 kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant, horizontal force of 19.6 N.
Find the speed of the block after it has moced 4.72 m.
Answer in units of m/s.
a = F/M = 19.6/2.25 = 8.71 m/s^2.
V^2 = Vo^2 + 2a*d.
Vo = 0.
V = ?
To find the speed of the block after it has moved 4.72 m, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be written as:
Work = Change in Kinetic Energy
In this case, the work done on the block is equal to the product of the force applied and the distance it moves:
Work = Force * Distance
Substituting the values given in the problem:
Work = 19.6 N * 4.72 m
Next, we need to know the relationship between work and the change in kinetic energy. The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Since the block is initially at rest, its initial kinetic energy is zero.
Therefore, the change in kinetic energy is equal to the final kinetic energy.
Now, we can set up the equation using the work-energy principle:
Work = Change in Kinetic Energy
19.6 N * 4.72 m = Final Kinetic Energy
To find the speed (final kinetic energy) of the block, we can use the equation:
Final Kinetic Energy = (1/2) * mass * speed^2
Substituting the values into the equation:
19.6 N * 4.72 m = (1/2) * 2.25 kg * speed^2
Solving for the speed, we have:
speed^2 = (19.6 N * 4.72 m) / (0.5 * 2.25 kg)
speed^2 = 196.28 Nm / 2.25 kg
speed^2 = 87.24 m^2/s^2
Taking the square root of both sides, we get:
speed = sqrt(87.24 m^2/s^2)
Therefore, the speed of the block after it has moved 4.72 m is approximately 9.35 m/s.