in a lab, a block weighing 80 n is attached to a spring scale, and both are pulled to the right on a horizontal surface, as shown above. friction between the block and the surface is negligible. what is the acceleration of the block when the scale reads 32 n?
The Correct Answer and Explanation is:
To determine the acceleration of the block, we use Newton’s Second Law of Motion:
F = ma
Where:
- F is the net force acting on the object (in newtons)
- m is the mass of the object (in kilograms)
- a is the acceleration (in meters per second squared)
Step 1: Find the mass of the block
The weight of the block is given as 80 N. Weight is related to mass by the equation:
Weight = mass × gravity
80 N = m × 9.8 m/s²
Solving for mass:
m = 80 / 9.8 ≈ 8.16 kg
Step 2: Use Newton’s Second Law
Now, apply F = ma with the net force equal to the spring scale reading, which is 32 N:
32 N = 8.16 kg × a
Solving for acceleration:
a = 32 / 8.16 ≈ 3.92 m/s²
Final Answer:
The acceleration of the block is approximately 4.0 m/s²
Explanation:
Since the surface is frictionless, the only horizontal force acting on the block is the 32 N tension from the spring scale. This means that the entire force is used to accelerate the block. By converting the weight to mass using Earth’s gravity and applying Newton’s second law, we determine how quickly the velocity of the block increases. Rounding the result gives us 4.0 m/s², which matches answer choice:
C. 4.0 m/s²
This analysis assumes ideal lab conditions with no friction and a horizontal plane, which simplifies the calculations and allows direct use of the scale’s reading as the net force.
