Q: A 10.0-kg box rests on a horizontal floor. If the coefficient of static friction is $$\mu_s = 0.40$$, what is the maximum static friction force before the box starts to move?

$$F_{fr(max)} = \mu_s F_N = 0.40 \times 98.0 = 39.2\ \mathrm{N}$$

Q: A 1500-kg car is brought to rest from $$27.8\ \mathrm{m/s} in$$ $$55\ \mathrm{m}. $$What is the average net force required to stop the car?

$$F = ma = m \left( \frac{v_f^2$ - v_i^2$}{2x} \right) = 1500 \times \left( \frac{0 - (27.8)^2$}{2 \times 55} \right) = -10500\ \mathrm{N}$$

Question 1

A rocket launches into space, expelling hot gases backward as shown in the image. According to Newton's Third Law, what is the reaction force to the rocket pushing on the gases?

Accepted Answer

The gases push forward on the rocket with an equal and opposite force.

Question 2

A car suddenly starts moving forward, and the passengers are pushed back into their seats. Which law of motion best explains this phenomenon?

Accepted Answer

Newton's First Law (Law of Inertia)

Question 3

In the diagram showing applied forces and net force, if two forces of 5 N each act in opposite directions on a box, what is the net force?

Accepted Answer

$$0\ \mathrm{N}$$

Question 4

Two people pull a boat with forces $$F_A = 40.0\ \mathrm{N} at$$ $$45.0^\circ$$ and $$F_B = 30.0\ \mathrm{N} at$$ $$37.0^\circ as $$shown. What is the best method to find the net force on the boat?

Accepted Answer

Resolve each force into x and y components, sum the components, and use the Pythagorean theorem to find the magnitude.

Question 5

A box is at rest on a table. The table exerts an upward normal force on the box, and the box exerts a downward force on the table. According to Newton's Third Law, these forces are:

Accepted Answer

Equal in magnitude and opposite in direction, acting on different objects.

Question 6

A 10.0-kg box is pulled along a frictionless surface with a force of $$40.0\ \mathrm{N} at$$ $$30^\circ$$ above the horizontal. What is the horizontal component of the pulling force?

Accepted Answer

$$40.0\cos 30^\circ = 34.6\ \mathrm{N}$$

Question 7

A 10.0-kg box rests on a horizontal floor. If the coefficient of static friction is $$\mu_s = 0.40$$, what is the maximum static friction force before the box starts to move?

Accepted Answer

$$F_{fr(max)} = \mu_s F_N = 0.40 	imes 98.0 = 39.2\ \mathrm{N}$$

Question 8

A 1500-kg car is brought to rest from $$27.8\ \mathrm{m/s} in$$ $$55\ \mathrm{m}. $$What is the average net force required to stop the car?

Accepted Answer

$$F = ma = m \left( \frac{v_f^2$ - v_i^2$}{2x} ight) = 1500 	imes \left( \frac{0 - (27.8)^2$}{2 	imes 55} ight) = -10500\ \mathrm{N}$$

Question 9

A person pushes a box with a force of $$75\ \mathrm{N} to $$the right, and the friction force is $$75\ \mathrm{N} to $$the left. What is the acceleration of the box?

Accepted Answer

Zero, because the net force is zero.

Question 10

A 10.0-kg box is held against a rough vertical wall. If $$\mu_s = 0.40$$, what is the minimum force $$F$$ required to keep the box from falling?

Accepted Answer

$$F = \frac{mg}{\mu_s} = \frac{98.0}{0.40} = 245\ \mathrm{N}$$

Question 11

A skier descends a $$30^\circ$$ slope with $$\mu_k = 0.10. $$What is her acceleration down the slope?

Accepted Answer

$$a = g(\sin 30^\circ - \mu_k \cos 30^\circ) = 9.8(0.5 - 0.10 	imes 0.866) = 4.0\ \mathrm{m/s}^2$$

Question 12

A 1150-kg elevator is connected to a 1000-kg counterweight over a frictionless pulley. What is the acceleration of the elevator?

Accepted Answer

$$a = \frac{(m_E - m_C)g}{m_E + m_C} = \frac{(1150 - 1000) 	imes 9.8}{1150 + 1000} = 0.68\ \mathrm{m/s}^2$$

Question 13

A 10.0-kg box is pulled along a table with a force of $$40.0\ \mathrm{N} at$$ $$30^\circ$$ and moves with an acceleration of $$1.12\ \mathrm{m/s}^2. $$What is the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = \frac{F_{fr}}{F_N} = \frac{23.4}{78.0} = 0.30$$

Question 14

Which of the following statements about action and reaction forces is correct?

Accepted Answer

They act on different objects and are equal in magnitude and opposite in direction.

Question 15

A 1.0-kg object weighs 9.8 N on Earth and 1.7 N on the Moon. What property of the object changes between Earth and Moon?

Accepted Answer

Weight

Question 16

A person stands on a scale in an elevator accelerating upward. Compared to when the elevator is at rest, the scale reading will:

Accepted Answer

Increase

Question 17

A box is at rest on a table. Which of the following is NOT an action-reaction pair according to Newton's Third Law?

Accepted Answer

The normal force exerted by the table on the box and the weight of the box.

Dynamics: Newton’s Laws of Motion – Structured Study Notes

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