Question 1

Two crates, one with mass $$6.00\ \mathrm{kg}$$ and the other with mass $$4.00\ \mathrm{kg}$$, are connected by a light string and pulled with a force $$F on a $$frictionless surface. If the acceleration of the system is $$2.50\ \mathrm{m/s^2$}$$, what is the net force acting on the entire system?

Accepted Answer

$$25.0\ \mathrm{N}$$

Question 2

Given the same system, what is the acceleration of the $$4.00\ \mathrm{kg}$$ crate?

Accepted Answer

$$2.50\ \mathrm{m/s^2$}$$

Question 3

What is the tension $$T in $$the string connecting the two crates?

Accepted Answer

$$10.0\ \mathrm{N}$$

Question 4

Which of the following best explains why the tension in the string is less than the applied force $$F$$?

Accepted Answer

The tension only needs to accelerate the $$4.00\ \mathrm{kg}$$ crate, not both crates.

Question 5

If the force $$F is $$suddenly removed, what happens to the tension in the string?

Accepted Answer

It immediately drops to zero.

Question 6

Which equation correctly represents Newton's Second Law for the $$4.00\ \mathrm{kg}$$ crate?

Accepted Answer

$$T = m a$$

Question 7

If the mass of the second crate is doubled, what happens to the acceleration of the system (assuming the same applied force $$F$$)?

Accepted Answer

The acceleration decreases.

Question 8

Which of the following is a correct application of Newton's Second Law to the entire system?

Accepted Answer

$$F = (m_1$ + m_2$)a$$

Question 9

If the string connecting the crates can withstand a maximum tension of $$12.0\ \mathrm{N}$$, what is the maximum acceleration the system can have before the string breaks?

Accepted Answer

$$3.00\ \mathrm{m/s^2$}$$

Question 10

If the surface was not frictionless and the coefficient of kinetic friction was $$\mu_k = 0.10$$, what would be the new net force required to maintain the same acceleration?

Accepted Answer

$$F = (m_1$ + m_2$)a + \mu_k (m_1$ + m_2$)g$$

Newton’s Second Law and Tension in Connected Masses (Physics with Calculus)

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