Q: A block slides down an inclined plane with angle $$\theta$$ and coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

$$a = g \sin \theta - \mu_k g \cos \theta$$

Q: A block of mass $$m is $$sliding down a ramp at angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$Which equation gives the net force acting on the block?

$$F_{net} = m g \sin \theta - \mu_k m g \cos \theta$$

Q: A block of mass $$m_1 is $$connected to a block of mass $$m_2 on an $$inclined plane at angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. If$$ $$m_1$$ hangs vertically and $$m_2 is on $$the incline, what is the acceleration of the system?

$$a = \frac{m_1$ g - m_2$ g \sin \theta - \mu_k m_2$ g \cos \theta}{m_1$ + m_2$}$$

Question 1

Which of the following correctly describes the difference between static and kinetic friction?

Accepted Answer

Static friction acts when surfaces are not moving relative to each other, while kinetic friction acts when surfaces are moving relative to each other.

Question 2

Given the equation for kinetic friction $$F_{kf} = \mu_k N$$, what does $$N$$ represent?

Accepted Answer

The normal force exerted by the surface on the object.

Question 3

A box of mass $$m is $$pulled across a horizontal surface with a constant velocity. If the coefficient of kinetic friction is $$\mu_k$$, what is the magnitude of the applied force?

Accepted Answer

$$F = \mu_k m g$$

Question 4

A block of mass $$m_1$$ hangs from a rope connected to a block of mass $$m_2 on a $$frictionless table. If $$m_1 is $$released, what is the acceleration of the system?

Accepted Answer

$$a = \frac{m_1$ g}{m_1$ + m_2$}$$

Question 5

A block slides down an inclined plane with angle $$	heta$$ and coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin 	heta - \mu_k g \cos 	heta$$

Question 6

The drag force on an object moving through air is given by $$F_D = \frac{1}{2} C_D \rho A v^2$. Which variable does NOT affect the drag force?

Accepted Answer

The mass of the object.

Question 7

At terminal velocity, which of the following is true for an object falling through air?

Accepted Answer

The drag force equals the gravitational force.

Question 8

Given the equation for terminal velocity $$v_t = \sqrt{\frac{2mg}{C_D \rho A}}$$, which change will increase the terminal velocity of a falling object?

Accepted Answer

Decreasing the air density $$\rho.$$

Question 9

A puck of mass $$m$$ moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of the centripetal force acting on the puck?

Accepted Answer

$$F = \frac{m v^2$}{r}$$

Question 10

If a block is moving in a circle at constant speed, what is the direction of its acceleration?

Accepted Answer

Radially inward toward the center.

Question 11

A block of mass $$m_2 is $$attached to a string and moves in a horizontal circle of radius $$r at $$speed $$v. $$The tension in the string is $$T. $$What is the relationship between $$T$$, $$m_2$$, $$v$$, and $$r$$?

Accepted Answer

$$T = \frac{m_2$ v^2$}{r}$$

Question 12

A block of mass $$m is $$dropped from height $$h. $$Neglecting air resistance, what is the time it takes to reach the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 13

A block of mass $$m is $$sliding down a ramp at angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$Which equation gives the net force acting on the block?

Accepted Answer

$$F_{net} = m g \sin 	heta - \mu_k m g \cos 	heta$$

Question 14

If the coefficient of static friction between a block and a surface is $$\mu_s$$, what is the maximum force that can be applied before the block starts to move?

Accepted Answer

$$F_{max} = \mu_s N$$

Question 15

A car of mass $$m is $$moving at constant speed $$v$$ around a flat circular track of radius $$r. $$What is the minimum coefficient of static friction $$\mu_s$$ required to prevent the car from sliding?

Accepted Answer

$$\mu_s = \frac{v^2$}{g r}$$

Question 16

A block of mass $$m is $$pulled by a force $$F at an $$angle $$	heta$$ above the horizontal on a rough surface with coefficient of kinetic friction $$\mu_k. $$What is the normal force $$N$$ acting on the block?

Accepted Answer

$$N = m g - F \sin 	heta$$

Question 17

A block of mass $$m_1 is $$connected to a block of mass $$m_2 on an $$inclined plane at angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. If$$ $$m_1$$ hangs vertically and $$m_2 is on $$the incline, what is the acceleration of the system?

Accepted Answer

$$a = \frac{m_1$ g - m_2$ g \sin 	heta - \mu_k m_2$ g \cos 	heta}{m_1$ + m_2$}$$

Question 18

A block moves in a circle of radius $$r at $$constant speed $$v. If $$the mass of the block is doubled, what happens to the required centripetal force?

Accepted Answer

It is doubled.

Forces, Friction, Drag, and Circular Motion: Study Notes

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