Q: A block slides down a ramp inclined at an angle $$\theta$$ with the horizontal. What is the net force along the axis parallel to the ramp (x'-axis) if the block experiences gravity $$F_g$$, normal force $$N$$, and kinetic friction $$f_k$$?

$$F_{x'} = mg \sin\theta - f_k$$

Question 1

Which of the following lists the three base dimensions used in classical mechanics in the SI system?

Accepted Answer

Length, mass, and time

Question 2

What are the dimensions of volume in terms of length (L), mass (M), and time (T)?

Accepted Answer

$$L^3$$

Question 3

What are the dimensions of speed?

Accepted Answer

$$L T$$^{-1}$$

Question 4

A block slides down a ramp inclined at an angle $$	heta$$ with the horizontal. What is the net force along the axis parallel to the ramp (x'-axis) if the block experiences gravity $$F_g$$, normal force $$N$$, and kinetic friction $$f_k$$?

Accepted Answer

$$F_{x'} = mg \sin	heta - f_k$$

Question 5

Approximately what is the mass of the average adult in kilograms?

Accepted Answer

80 kg

Question 6

If a vector $$\vec{A}$$ has a magnitude of 10 and a direction angle of $$60^\circ$$, what are the magnitude and direction angle of $$-\vec{A}$$?

Accepted Answer

10, $$240^\circ$$

Question 7

Which of the following is a valid procedure for determining the components of a vector in a given coordinate system?

Accepted Answer

Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with $$\phi as $$the included angle.

Question 8

A physics student has four equations with five unknowns and is asked to solve for $$a_2. $$What is the correct strategy?

Accepted Answer

Eliminate all unknowns except $$a_2$$ using substitution.

Question 9

A vector $$\vec{F}$$ has a magnitude $$F$$ and makes an angle $$\phi$$ with the x-axis. What are its x and y components?

Accepted Answer

$$F \cos\phi, F \sin\phi$$

Question 10

A torque is exerted by a force $$\vec{F} of $$magnitude 4.0 N at an angle of $$36^\circ$$ from the x-axis, applied at a point 22.0 cm from the axis of rotation. What is the magnitude of the torque?

Accepted Answer

$$0.52\ \mathrm{N \cdot m}$$

Question 11

Which of the following is NOT a valid operation in dimensional analysis?

Accepted Answer

Adding quantities with different dimensions

Question 12

A car travels 10,000 miles per year and gets 20 miles per gallon. If there are two cars for every three people in the US, and the population is 330 million, approximately how many gallons of gasoline are used per day?

Accepted Answer

$$6.13 	imes 10^8$ gal/day

Question 13

A block of mass $$m$$ slides down a frictionless incline at angle $$	heta. $$What is the acceleration of the block?

Accepted Answer

$$g \sin	heta$$

Question 14

Which of the following best describes the direction of the displacement vector from $$(1,0) to$$ $$(0,2)$$?

Accepted Answer

The vector points upward and to the left.

Question 15

Which of the following is the correct simplification of $$\vec{A} + \vec{B} - \vec{A}$$ using vector laws?

Accepted Answer

$$\vec{B}$$

Question 16

When resolving a vector into components in a rotated coordinate system, what must you always consider?

Accepted Answer

The signs of the components based on the quadrant

Question 17

Which of the following is a derived unit in the SI system?

Accepted Answer

Newton

Physics with Calculus: Units, Physical Quantities, and Vectors – Step-by-Step Study Guidance

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