Question 1

A block is subjected to two forces: $$\vec{F}_1 = (3.0\,\mathrm{N})\,\hat{i} + (4.0\,\mathrm{N})\,\hat{j}$$ and $$\vec{F}_2 = (-3.0\,\mathrm{N})\,\hat{i} + (4.0\,\mathrm{N})\,\hat{j}. If $$the block has a mass of $$2.0\,\mathrm{kg}$$, what is the magnitude of its acceleration?

Accepted Answer

$$4.0\,\mathrm{m/s^2$}$$

Question 2

Two horizontal forces act on a $$3.0\,\mathrm{kg}$$ object moving on a horizontal surface with negligible friction. Force $$\vec{F}_1 = 3.0\,\mathrm{N}$$ acts along the east, and force $$\vec{F}_2 = 8.0\,\mathrm{N}$$ acts $$62^\circ$$ north of west. What is the magnitude of the object's acceleration?

Accepted Answer

$$3.5\,\mathrm{m/s^2$}$$

Question 3

A $$2.0\,\mathrm{kg}$$ object moves along the $$x-$$axis, being propelled by a variable force $$F = 3.0t + (4.0t^2$) - (0.2t^3$)$$, where $$F is in $$newtons and $$t is in $$seconds. At $$t = 3.0\,\mathrm{s}$$, the force on the particle has a magnitude of $$36\,\mathrm{N} in $$the negative $$x-$$direction. What is the value of the constant $$c in $$the force equation?

Accepted Answer

$$c = -0.2$$

Question 4

In the arrangement shown, four disks are suspended by cords. The top cord supports a total weight of $$100\,\mathrm{N}$$, and the tensions in the shorter cords are $$T_1 = 60$$\,\mathrm{N}$$, T_2$ = 50\,\mathrm{N}$$, and $$T_3 = 10$$\,\mathrm{N}$$. What is the mass of disk D?

Accepted Answer

$$10.0\,\mathrm{kg}$$

Question 5

In the same arrangement, what is the mass of disk B if the tension in its supporting cord is $$T_2 = 50$$\,\mathrm{N}$$?

Accepted Answer

$$5.0\,\mathrm{kg}$$

Question 6

An Atwood's machine consists of two blocks connected by a cord over a frictionless pulley. Block 1 has mass $$m_1 = 1.30$$\,\mathrm{kg}$$ and block 2 has mass m_2$ = 2.80\,\mathrm{kg}. $$What is the acceleration of the system?

Accepted Answer

$$a = \dfrac{m_2$ - m_1$}{m_1$ + m_2$}g$$

Question 7

For the Atwood's machine above, what is the tension in the cord?

Accepted Answer

$$T = \dfrac{2m_1 m_2$}{m_1$ + m_2$}g - m_1$ a$$

Question 8

Three blocks are connected by cords, one of which wraps over a pulley. The masses are $$m_A = 30\,\mathrm{kg}$$, $$m_B = 40\,\mathrm{kg}$$, and $$m_C = 10\,\mathrm{kg}. If $$the system starts from rest, what is the acceleration of block A?

Accepted Answer

$$a = \dfrac{(m_B - m_C)g}{m_A + m_B + m_C}$$

Question 9

In the three-block system above, what is the tension in the cord connecting blocks B and C?

Accepted Answer

$$T = m_C g - m_C a$$

Question 10

A $$10\,\mathrm{kg}$$ disk is suspended by a cord. What is the tension in the cord?

Accepted Answer

$$100\,\mathrm{N}$$

Question 11

A block of mass $$m is $$pulled by a force $$F on a $$frictionless surface. If $$F is $$doubled, what happens to the acceleration?

Accepted Answer

It doubles

Question 12

A $$2.0\,\mathrm{kg}$$ object is acted on by a force $$F = 3.0t + 4.0t^2$ - 0.2t^3$. What is the acceleration at t = 2.0$$\,\mathrm{s}$$?

Accepted Answer

$$a = 6.4\,\mathrm{m/s^2$}$$

Question 13

A $$3.0\,\mathrm{kg}$$ object is pulled by a $$9.0\,\mathrm{N}$$ force at an angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the acceleration?

Accepted Answer

$$a_x = 2.6\,\mathrm{m/s^2$}$$

Question 14

In a real-world scenario, a rescue worker pulls a $$50\,\mathrm{kg}$$ sled with a rope at $$20^\circ$$ above the horizontal, exerting a force of $$200\,\mathrm{N}. $$What is the horizontal acceleration of the sled (neglecting friction)?

Accepted Answer

$$a = 3.76\,\mathrm{m/s^2$}$$

Question 15

A $$5.0\,\mathrm{kg}$$ box is pushed with a force of $$25\,\mathrm{N} on a $$frictionless surface. What is its acceleration?

Accepted Answer

$$5.0\,\mathrm{m/s^2$}$$

Question 16

A $$2.0\,\mathrm{kg}$$ object is acted on by a force $$F = 3.0t + 4.0t^2$ - 0.2t^3$. What is the velocity at t = 1.0$$\,\mathrm{s}$$ if it starts from rest?

Accepted Answer

$$v = 3.9\,\mathrm{m/s}$$

Question 17

A $$10\,\mathrm{kg}$$ disk is suspended by a cord. If the cord is cut, what is the acceleration of the disk immediately after?

Accepted Answer

$$9.8\,\mathrm{m/s^2$}$$

Forces, Free-Body Diagrams, and Newtonian Mechanics: Study Notes

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