Q: A block of mass $$m_1$$ sits on a frictionless inclined plane at angle $$\theta$$ and is connected by a massless rope over a massless, frictionless pulley to a hanging mass $$m_2. $$What value of $$m_2$$ will keep $$m_1$$ from moving?

$$m_2$$ = $$m_1$$ \sin \theta$$

Q: A 5 kg object is suspended from a spring scale in an elevator accelerating upward at $$2\,\mathrm{m/s^2$}. $$What does the scale read?

$$F = m(g + a) = 5 \times (9.8 + 2) = 59\,\mathrm{N}$$

Q: A block is at rest on a frictionless incline. If the incline angle increases, what happens to the normal force?

The normal force decreases because $$F_N = mg \cos \theta.$$

Q: A 2 kg block is on a frictionless incline at $$45^\circ. $$What is the component of the gravitational force parallel to the incline?

$$F_{\parallel} = mg \sin \theta = 2 \times 9.8 \times \sin 45^\circ$$

Question 1

A snowboarder with mass 72.9 kg glides down a frictionless slope inclined at $$	heta = 22^\circ to $$the horizontal. What is the snowboarder's acceleration down the slope?

Accepted Answer

$$a = g \sin 	heta$$

Question 2

Which of the following best describes the difference between mass and weight?

Accepted Answer

Mass is an intrinsic property, while weight depends on the local gravitational field.

Question 3

A block of mass $$m_1$$ sits on a frictionless inclined plane at angle $$	heta$$ and is connected by a massless rope over a massless, frictionless pulley to a hanging mass $$m_2. $$What value of $$m_2$$ will keep $$m_1$$ from moving?

Accepted Answer

$$m_2$$ = $$m_1$$ \sin 	heta$$

Question 4

If the angle $$	heta of $$the inclined plane is $$0^\circ$$, what happens to the equilibrium of the system described above?

Accepted Answer

There can be no equilibrium; block 1 will slide no matter what.

Question 5

A 10 kg box is placed on a frictionless incline at $$30^\circ. $$What is the normal force acting on the box?

Accepted Answer

$$F_N = mg \cos 	heta$$

Question 6

A scale measures the weight of an object. If the object is taken to the Moon, where $$g_{moon} \approx 1.6\,\mathrm{m/s^2$}$$, what happens to the reading on the scale?

Accepted Answer

The reading decreases because weight depends on the local gravitational field.

Question 7

A block is at rest on a frictionless incline. Which of the following statements is true about the forces acting on the block?

Accepted Answer

The normal force and the component of gravity perpendicular to the incline are equal in magnitude.

Question 8

A 5 kg object is suspended from a spring scale in an elevator accelerating upward at $$2\,\mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$F = m(g + a) = 5 	imes (9.8 + 2) = 59\,\mathrm{N}$$

Question 9

Which of the following is the correct application of Newton’s Second Law for a block sliding down a frictionless incline?

Accepted Answer

$$m a = m g \sin 	heta$$

Question 10

A block of mass $$m is at $$rest on a horizontal surface. What is the normal force acting on the block?

Accepted Answer

$$F_N = mg$$

Question 11

A block of mass $$m_1 is on a $$frictionless incline at angle $$	heta$$ and connected to a hanging mass $$m_2 by a $$massless rope over a pulley. If $$m_2$$ \u003e $$m_1$$ \sin 	heta$$, what will happen?

Accepted Answer

The system will accelerate, with $$m_2$$ descending and $$m_1$$ ascending the incline.

Question 12

Which of the following best describes the force measured by a spring scale when an object is stationary?

Accepted Answer

The force measured is the weight of the object.

Question 13

A block is at rest on a frictionless incline. If the incline angle increases, what happens to the normal force?

Accepted Answer

The normal force decreases because $$F_N = mg \cos 	heta.$$

Question 14

A 2 kg block is on a frictionless incline at $$45^\circ. $$What is the component of the gravitational force parallel to the incline?

Accepted Answer

$$F_{\parallel} = mg \sin 	heta = 2 	imes 9.8 	imes \sin 45^\circ$$

Question 15

A block is connected to a hanging mass by a rope over a pulley. If the system is in equilibrium, which of the following must be true?

Accepted Answer

The net force on each block is zero.

Equilibrium and Newton’s Second Law: Inclined Planes and Pulley Systems

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