A 3.8 kg block initially at rest is pulled to the
right along a horizontal, frictionless surface
by a constant, horizontal force of 13.5 N.
Find the speed of the block after it has
moved 4.22 m.
Answer in units of m/s
To find the speed of the block after it has moved 4.22 m, you can use the concept of work and energy.
The work done on an object is equal to the force applied on it multiplied by the distance it moves in the direction of the applied force. In this case, the force is 13.5 N and the distance is 4.22 m.
The work done on the block can be calculated using the formula:
Work = Force × Distance
So, the work done on the block is:
Work = 13.5 N × 4.22 m
Now, according to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy (energy due to motion). Mathematically, it can be expressed as:
Work = Change in Kinetic Energy
So, we can equate the work done on the block to the change in its kinetic energy:
13.5 N × 4.22 m = Change in Kinetic Energy
Now, we need to find the change in kinetic energy. The initial kinetic energy of the block is zero since it is initially at rest.
So, the change in kinetic energy = Final Kinetic Energy - Initial Kinetic Energy
Since the initial kinetic energy is zero, the change in kinetic energy is equal to the final kinetic energy. Therefore, we can rewrite the equation as:
13.5 N × 4.22 m = Final Kinetic Energy
Now, we can solve for the final kinetic energy:
Final Kinetic Energy = (13.5 N × 4.22 m)
The final kinetic energy can be calculated by multiplying the force (13.5 N) by the distance (4.22 m).
Once you have the final kinetic energy, you can use the formula for kinetic energy to find the speed of the block:
Final Kinetic Energy = 0.5 × mass × (speed)^2
In this case, the mass of the block is given as 3.8 kg:
0.5 × 3.8 kg × (speed)^2 = Final Kinetic Energy
Now, you can solve this equation for the speed of the block. Rearranging the equation, we get:
(speed)^2 = (2 × Final Kinetic Energy) / mass
Substituting the values, we get:
(speed)^2 = (2 × (13.5 N × 4.22 m)) / 3.8 kg
Now, you can calculate the square root of both sides of the equation to find the speed of the block:
speed = √[(2 × (13.5 N × 4.22 m)) / 3.8 kg]
By evaluating this expression, you will obtain the speed of the block after it has moved 4.22 m.