A 5kg block is being pulled on a horizontal frictionless surface. The tension in the string is 30N. If the block has an initial speed of 2m/s, what is the speed after moving 10 meters?
Please help!Thanks
a = F/m
vf^2 -vi^2 = 2ax
solve for vf
11.16ms-1
To find the final speed of the block after moving 10 meters, we can use the concept of work and energy.
First, let's calculate the work done on the block. Work is defined as the product of force and displacement, given by the formula:
Work = Force * Displacement * cos(theta)
In this case, since the force applied (tension) and displacement are in the same direction, the angle between them is 0 degrees, which means cos(theta) is equal to 1. We can therefore simplify the formula to:
Work = Force * Displacement
The work done is equal to the change in kinetic energy of the block. So, we have:
Work = Change in Kinetic Energy
The initial kinetic energy of the block is given by the formula:
Kinetic Energy = (1/2) * mass * initial velocity^2
Substituting the given values:
Kinetic Energy = (1/2) * 5kg * (2m/s)^2 = 10 Joules
Now, we can find the work done:
Work = Change in Kinetic Energy = 10 Joules
Since work is equal to the force multiplied by the displacement, we have:
Work = Force * Displacement
30N * 10m = 300 Joules
Therefore, the work done on the block to move it 10 meters is 300 Joules.
Now, using the work-energy principle, we can find the final kinetic energy of the block. The final kinetic energy is equal to the initial kinetic energy plus the work done:
Final Kinetic Energy = Initial Kinetic Energy + Work
Final Kinetic Energy = 10 Joules + 300 Joules = 310 Joules
Finally, we can find the final speed by rearranging the kinetic energy formula:
Final Kinetic Energy = (1/2) * mass * final velocity^2
Substituting the given values:
310 Joules = (1/2) * 5kg * final velocity^2
Rearranging the equation and solving for final velocity:
final velocity = sqrt(310 Joules * 2 / 5kg) = sqrt(124) ≈ 11.14m/s
Therefore, the final speed of the block after moving 10 meters is approximately 11.14 m/s.