Question

Given the net forces on and the masses of the blocks shown above, which two blocks have the same acceleration? Select two answers.

A)Block A
B)Block B
C)Block C
D)Block D

Answer 1

Answer:

Selected answers A) and D)

Explanation:

Acceleration

According to the Newton's second law of motion, the acceleration of an object is directly proportional to the net force F and inversely proportional to the object's mass:

$\displaystyle a=\frac{F}{m}$

We are given four situations, let's compute the acceleration on each case.

A) The block A has a mass of m=5 kg and a net force of F=20 N. The acceleration is:

$\displaystyle a=\frac{20}{5}=4\ m/s^2$

This option must be selected because the acceleration is the same as the option D. Correct option A

B) The block B has a mass of m=10 kg and a net force of F=25 N. The acceleration is:

$\displaystyle a=\frac{25}{10}=2.5\ m/s^2$

No other option has this value of acceleration, so this option is not correct.

C) The block C has a mass of m=20 kg and a net force of F=100 N. The acceleration is:

$\displaystyle a=\frac{100}{20}=5\ m/s^2$

No other option has this value of acceleration, so this option is not correct.

D) The block D has a mass of m=20 kg and a net force of F=80 N. The acceleration is:

$\displaystyle a=\frac{80}{20}=4\ m/s^2$

This option must be selected because the acceleration is the same as the option A. Correct option D

Answer 2

Block A (m = 5kg; F = 20 N) and Block D (m = 20 kg; F = 80 N) have the same acceleration.

Acceleration (a) is the change in velocity over time.

It is directly proportional to the force applied (F) and inversely proportional to the mass of the object (m).

We can calculate the acceleration of each block using Newton's second law of motion.

$a = \frac{F}{m}$

Block A

$a = \frac{F}{m} = \frac{20N}{5kg} = 4m/s^{2}$

Block B

$a = \frac{F}{m} = \frac{25N}{10kg} = 2.5m/s^{2}$

Block C

$a = \frac{F}{m} = \frac{100N}{20kg} = 5m/s^{2}$

Block D

$a = \frac{F}{m} = \frac{80N}{20kg} = 4m/s^{2}$

Block A (m = 5kg; F = 20 N) and Block D (m = 20 kg; F = 80 N) have the same acceleration.

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