Question

Two boxes of textbooks, of masses 10 kg and 15 kg, are connected by a lightweight string, and then pulled across a horizontal table by a horizontal applied force, as shown in the diagram above (attached to question).

The applied force has a magnitude of 50 N, and there is no friction between the boxes and table. What is the acceleration of the 10 kg 10 kg box?

A.) 3.3 m/s^2
B.) 2.0 m/s^2
C.) 5.0 m/s^2
D.) The box will not accelerate because the tension force acting on it to the left must also be 50 N 50 N.

Answer 1

The acceleration of the 10 kg box is determined as 2 m/s². (Option B)

How to calculate the acceleration of the box?

The acceleration of the 10 kg box is calculated by applying Newton's second law of motion as follows;

F(net) = ma

where;

• m is the total mass of the system
• a is the acceleration of the system

The total mass of the two boxes is calculated as;

m = 15 kg + 10 kg

m = 25 kg

The acceleration of the 10 kg box is calculated as follows;

a = F(net) / m

a = ( 50 N ) / 25 kg

a = 2 m/s²

Thus, the acceleration of the system is 2 m/s².

Answer 2

The correct option is;

B.) 2.0 m/s²

Step-by-step explanation:

The given information are;

The masses of the boxes are; m₁ = 15 kg and m₂ = 10 kg

The force applied, F = 50 N

The friction force between the blocks and the table = N/A

The equation for the applied force, F = Mass, m × Acceleration, a

Therefore;

a = F/m

Given that the two boxes are attached to each other and to the force by a spring, they will experience the same motion, and therefore, the same acceleration

The total mass (the two blocks) pulled by the applied, 50 N force,
`m_T` = m₁ + m₂ = 10 kg + 15 kg = 25 kg

The acceleration given the blocks by the applied force, a = F/
`m_T` = 50 N/(25 kg) = 50 kg·m/s²/(25 kg) = 2 m/s²

The acceleration experienced by the 10 kg box = The acceleration experienced by the system of the two boxes = 2 m/s².