A dockworker applies a constant horizontal force of 90.0Nto a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves a distance 12.0min a time of 5.20s.If the worker stops pushing after 5.20s, how far does the block move in the next 5.30s
Vo = 12m/5.2s = 2.31 m/s.
Vf = 0.
a=(Vf-Vo)/t=(0-2.31)/5.30=-0.436 m/s^2.
d = Vo*t + 0.5a*t^2.
d = 2.31*5.3 - 0.218*(5.3)^2 = 6.1 m.
To determine how far the block moves in the next 5.30 seconds, we can use the concept of constant acceleration motion.
First, we need to calculate the acceleration of the block using the given information. The equation for acceleration is:
acceleration (a) = force (F) / mass (m)
In this case, the force applied by the dockworker is 90.0 N, and the mass of the block is not given. However, since the frictional force is negligible, there are no other forces acting on the block. Therefore, the applied force will also be equal to the force of inertia (force required to move an object with constant velocity), and we can use the formula:
force of inertia = mass (m) × acceleration (a)
Since the force of inertia is equal to the applied force of 90.0 N, we can rearrange the formula to solve for acceleration:
acceleration (a) = force of inertia / mass (m) = 90.0 N / mass (m)
Next, we need to find the initial velocity of the block. The block starts from rest, so its initial velocity (v0) is 0 m/s.
Using the equation of motion:
distance (d) = initial velocity (v0) × time (t) + 0.5 × acceleration (a) × time^2
For the first 5.20 seconds, we substitute the values for acceleration (a), initial velocity (v0), and time (t):
distance (d1) = 0 × 5.20 + 0.5 × acceleration (a) × 5.20^2
Now, we can calculate the distance the block moved during this time. However, we don't have the mass of the block, which means we cannot determine the acceleration or the distance traveled in the first 5.20 seconds. Without the mass, we cannot proceed to find the distance the block moves in the next 5.30 seconds.
Therefore, the given information is insufficient to calculate the distance the block moves in the next 5.30 seconds without knowing the mass of the block.