Question

"A force of 4 N produces an acceleration of 8 m/s^2 on a mass m1 and an acceleration of 16 m/s^2 on a mass m2. What acceleration in m/s^2 would the same force provide if both the masses are tied together? *

a] 4
b] 5.33
c] 24
d] 6"

Answer 1

When both masses m1 (0.5 kg) and m2 (0.25 kg) are tied together, the total mass is 0.75 kg. A force of 4 N acting on this combined mass would produce an acceleration of 5.33 m/s².

Step-by-step explanation:

The question asks for the acceleration of two masses when tied together and subjected to a certain force. This problem can be solved by understanding Newton's second law of motion, which states that force equals mass times acceleration (F = m*a). If a force of 4 N produces an acceleration of 8 m/s² on mass m1, we can calculate the mass m1 using the formula:

• F = m1 * a1
• 4 N = m1 * 8 m/s²
• m1 = 4 N / 8 m/s²
• m1 = 0.5 kg

Similarly, for mass m2:

• 4 N = m2 * 16 m/s²
• m2 = 4 N / 16 m/s²
• m2 = 0.25 kg

Now, when both masses are tied together, the total mass is m1 + m2 = 0.5 kg + 0.25 kg = 0.75 kg. The same force acting on combined mass would result in:

• F = (m1 + m2) * a
• 4 N = 0.75 kg * a
• a = 4 N / 0.75 kg
• a = 5.33 m/s²

Therefore, the acceleration when both masses are tied together is 5.33 m/s² (Option b).