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? A 2.0 m/s
B 2.5 m/s
C 4.0 m/s
D 6.0 m/s
E 8.0 m/s
The Correct Answer and Explanation is:
To find the acceleration of the block, we can use Newton’s Second Law of Motion:F=maF = maF=ma
Where:
- FFF is the net force acting on the object (in newtons)
- mmm is the mass of the object (in kilograms)
- aaa is the acceleration (in meters per second squared)
Step 1: Find the mass of the block
We are given the weight of the block as 80 N.
Weight is related to mass by the equation:W=mgW = mgW=mg
Where g=9.8 m/s2g = 9.8 \, \text{m/s}^2g=9.8m/s2 is the acceleration due to gravity.
So we can find the mass mmm:m=Wg=809.8≈8.16 kgm = \frac{W}{g} = \frac{80}{9.8} \approx 8.16 \, \text{kg}m=gW=9.880≈8.16kg
Step 2: Use Newton’s Second Law
The spring scale reads 32 N, which is the net force acting on the block since friction is negligible.
Now apply:F=ma⇒a=Fm=328.16≈3.92 m/s2F = ma \Rightarrow a = \frac{F}{m} = \frac{32}{8.16} \approx 3.92 \, \text{m/s}^2F=ma⇒a=mF=8.1632≈3.92m/s2
Step 3: Choose the closest answer
The closest choice to 3.92 m/s² is:
C. 4.0 m/s²
Final Answer: C. 4.0 m/s²
Explanation Summary
- The block’s weight gives us the mass using m=Wgm = \frac{W}{g}m=gW
- The spring scale reading represents the net force
- Using Newton’s Second Law, a=Fma = \frac{F}{m}a=mF, we find the acceleration
- The calculation gives about 3.92 m/s², which rounds to 4.0 m/s²
