A dock worker applies a constant horizontal force of 77.0 to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 9.00 in the first 7.00 .
What is the mass of the block of ice?
Do it in steps.
First compute the acceleration rate "a" from:
Average velocity = 9 m/7 s = 1.286 m/s
Final velocity = 2 x (average velocity)
Acceleration = (Final velocity)/7 s
Mass = Force/Acceleration
To find the mass of the block of ice, we can follow these steps:
Step 1: Compute the acceleration rate "a" using the given information.
- Average velocity = 9.00 m / 7.00 s = 1.286 m/s
- Final velocity = 2 x Average velocity = 2 x 1.286 m/s = 2.572 m/s
Acceleration = Final velocity / Time
Acceleration = 2.572 m/s / 7.00 s
Acceleration ≈ 0.3674 m/s²
Step 2: Calculate the force applied by the dock worker.
The given information states that a constant horizontal force of 77.0 N is applied to the block of ice.
Step 3: Determine the mass of the block using Newton's second law.
Newton's second law of motion states that Force (F) is equal to mass (m) multiplied by acceleration (a).
Mass (m) = Force (F) / Acceleration (a)
Mass = 77.0 N / 0.3674 m/s²
Using a calculator, we find that the mass of the block of ice is approximately 209.68 kg.