A dock worker applies a constant horizontal force of 79.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in the first 6.00 s.
What is the mass of the block of ice?
Work done = final kinetic energy
F X = (1/2) M V^2
The final velocity V is twice the average velocity of 11/6 m/s, so
V = 22/6 = 3.67 m/s
Solve for M
M = 2 F X/(V^2)
11.7
To find the mass of the block of ice, we can use the equation for work done and kinetic energy:
Work done (W) = final kinetic energy
The work done is given by the equation:
W = force (F) × distance (X)
In this case, the force applied by the dock worker is 79.0 N and the block of ice moves a distance of 11.0 m. Therefore, the work done is:
W = 79.0 N × 11.0 m
Next, we can calculate the final kinetic energy using the equation:
Final kinetic energy (KE) = (1/2) × mass (M) × velocity (V)^2
Since the block of ice starts from rest and moves 11.0 m in 6.00 s, we can find the average velocity:
Average velocity = distance / time = 11.0 m / 6.00 s
Then, the final velocity is twice the average velocity:
Final velocity (V) = 2 × (11.0 m / 6.00 s)
So, V = 22/6 = 3.67 m/s
Now, substituting the values into the equation for final kinetic energy:
Final kinetic energy (KE) = (1/2) × M × (3.67 m/s)^2
Since the work done is equal to the final kinetic energy, we can equate the two equations and solve for the mass (M):
79.0 N × 11.0 m = (1/2) × M × (3.67 m/s)^2
Now, solve for M:
M = (2 × 79.0 N × 11.0 m) / (3.67 m/s)^2
By calculating this expression, we can find the mass of the block of ice.