Newton's laws and forces — Hard Practice Quiz

A Physics cheat sheet for Newton's laws and forces — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Practice quiz

1. A block of mass $m$ is pulled horizontally across a rough surface by a force $P$. The coefficient of kinetic friction is $\mu_k$. If the pulling force $P$ is doubled to $2P$ and the mass $m$ is halved to $m/2$, what is the new acceleration $a'$ in terms of the original acceleration $a$, the original pulling force $P$, the original mass $m$, and the acceleration due to gravity $g$?

   • $a' = 4a + 3\mu_k g$
   • $a' = 2a + \mu_k g$
   • $a' = 4a - \mu_k g$
   • $a' = 2a + 2\mu_k g$

   Answer: $a' = 4a + 3\mu_k g$

2. An object has weight $W$ on the surface of Earth, which has mass $M_E$ and radius $R_E$. If this object is moved to a planet with mass $2M_E$ and radius $R_E/2$, what is its new weight $W_P$ in terms of $W$?

   • $W_P = 2W$
   • $W_P = 4W$
   • $W_P = 8W$
   • $W_P = 16W$

   Answer: $W_P = 8W$

3. Two blocks, $m_1$ and $m_2$, are in contact on a frictionless horizontal surface. A horizontal force $F$ is applied to $m_1$. Which of the following expressions correctly represents the magnitude of the force that $m_1$ exerts on $m_2$?

   • $\frac{F m_1}{m_1 + m_2}$
   • $\frac{F m_2}{m_1 + m_2}$
   • $F - m_1 a$
   • $F$

   Answer: $\frac{F m_2}{m_1 + m_2}$

4. A block of mass $m$ rests on an inclined plane. The coefficient of static friction between the block and the plane is $\mu_s$. What is the maximum angle $\theta$ of inclination for which the block remains at rest?

   • $\theta = \arcsin(\mu_s)$
   • $\theta = \arccos(\mu_s)$
   • $\theta = \arctan(\mu_s)$
   • $\theta = \frac{1}{\mu_s}$

   Answer: $\theta = \arctan(\mu_s)$

5. A block of mass $m$ is pulled by a rope at an angle $\phi$ above the horizontal. The tension in the rope is $T$. The coefficient of kinetic friction between the block and the surface is $\mu_k$. Which expression correctly describes the acceleration $a$ of the block?

   • $a = \frac{T \cos\phi - \mu_k (mg - T \sin\phi)}{m}$
   • $a = \frac{T \cos\phi - \mu_k mg}{m}$
   • $a = \frac{T \cos\phi + \mu_k (mg - T \sin\phi)}{m}$
   • $a = \frac{T \sin\phi - \mu_k mg}{m}$

   Answer: $a = \frac{T \cos\phi - \mu_k (mg - T \sin\phi)}{m}$

6. A satellite of mass $m$ orbits a planet of mass $M$ in a circular path of radius $r$. Which of the following expressions correctly represents the orbital speed $v$ of the satellite?

   • $v = \sqrt{\frac{GM}{r}}$
   • $v = \sqrt{\frac{Gm}{r}}$
   • $v = \frac{GM}{r}$
   • $v = \frac{Gm}{r^2}$

   Answer: $v = \sqrt{\frac{GM}{r}}$

7. A horse pulls a cart. According to Newton's Third Law, the force the horse exerts on the cart is equal in magnitude and opposite in direction to the force the cart exerts on the horse. If these forces are equal and opposite, how can the cart accelerate?

   • The horse's force on the cart is actually greater than the cart's force on the horse, despite Newton's Third Law.
   • The net force on the horse is zero, allowing it to pull the cart forward.
   • The cart accelerates because the net force acting *on the cart* (horse's pull minus friction) is non-zero, while the action-reaction pair acts on different objects.
   • The cart's wheels exert a force on the ground, which is the primary force propelling the cart forward.

   Answer: The cart accelerates because the net force acting *on the cart* (horse's pull minus friction) is non-zero, while the action-reaction pair acts on different objects.

8. A $10 \text{ kg}$ object is suspended by two ropes. One rope makes an angle of $30^\circ$ with the horizontal, and the other makes an angle of $60^\circ$ with the horizontal. Assuming $g = 10 \text{ m/s}^2$, what is the tension in the rope making the $30^\circ$ angle?

   • $50 \text{ N}$
   • $50\sqrt{3} \text{ N}$
   • $100 \text{ N}$
   • $25\sqrt{3} \text{ N}$

   Answer: $50 \text{ N}$

9. A block of mass $m$ is sliding on a horizontal surface with kinetic friction coefficient $\mu_k$. If an additional mass $m$ is placed on top of the block, how do the magnitude of the kinetic friction force $f_k$ and the magnitude of the acceleration $a$ (deceleration) change, assuming no other horizontal forces are applied?

   • The friction force doubles, and the acceleration doubles.
   • The friction force doubles, and the acceleration remains the same.
   • The friction force remains the same, and the acceleration halves.
   • The friction force halves, and the acceleration remains the same.

   Answer: The friction force doubles, and the acceleration remains the same.

10. A block of mass $m_1$ rests on a horizontal table with a coefficient of kinetic friction $\mu_k$. It is connected by a light string over a frictionless pulley to a hanging block of mass $m_2$. Which expression correctly represents the acceleration $a$ of the system?

    • $a = \frac{g(m_2 + \mu_k m_1)}{m_1 + m_2}$
    • $a = \frac{g(m_2 - \mu_k m_1)}{m_1 + m_2}$
    • $a = \frac{g m_2}{m_1 + m_2}$
    • $a = \frac{g(m_1 - \mu_k m_2)}{m_1 + m_2}$

    Answer: $a = \frac{g(m_2 - \mu_k m_1)}{m_1 + m_2}$