Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal, as shown in the first image. Neglecting air resistance, what is the formula for the horizontal range $$R of $$the projectile?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Q: A block is pulled across a rough surface at constant speed by a force $$F_{ext} at an $$angle $$\theta$$ above the horizontal. Which equation correctly relates the friction force $$f_k$$, the normal force $$N$$, and the weight $$mg$$?

$$N = mg - F_{ext} \sin \theta$$

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal, as shown in the first image. Neglecting air resistance, what is the formula for the horizontal range $$R of $$the projectile?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 2

In the scenario depicted in the second image, a truck is pulling a trailer and both are accelerating to the right. According to Newton's Third Law, how does the force exerted by the truck on the trailer compare to the force exerted by the trailer on the truck?

Accepted Answer

The forces are equal in magnitude and opposite in direction.

Question 3

A person stands in an elevator moving upward at constant speed, as shown in the image. What is the relationship between the normal force $$N$$ exerted by the floor and the person's weight $$W$$?

Accepted Answer

$$N = W$$

Question 4

A person stands in an elevator that is accelerating upward. What is the relationship between the normal force $$N$$ exerted by the floor and the person's weight $$W$$?

Accepted Answer

$$N \u003e W$$

Question 5

In the coordinate system shown, what is the $$y-$$component of the weight vector $$\vec{W} = mg$$?

Accepted Answer

$$W_y = -mg \cos 	heta$$

Question 6

A block of mass $$m is on an $$inclined plane at angle $$	heta$$ with the horizontal. What is the normal force $$N$$ acting on the block?

Accepted Answer

$$N = mg \cos 	heta$$

Question 7

A block of mass $$m is at $$rest on a rough incline with angle $$	heta$$ and coefficient of static friction $$\mu_s. $$What is the maximum angle $$	heta_{max}$$ before the block starts to slide?

Accepted Answer

$$	an 	heta_{max} = \mu_s$$

Question 8

In the Atwood's machine shown, mass $$A is $$less than mass $$B. $$What is the correct expression for the acceleration $$a of $$the system?

Accepted Answer

$$a = g \frac{m_B - m_A}{m_A + m_B}$$

Question 9

A block is pulled across a rough surface at constant speed by a force $$F_{ext} at an $$angle $$	heta$$ above the horizontal. Which equation correctly relates the friction force $$f_k$$, the normal force $$N$$, and the weight $$mg$$?

Accepted Answer

$$N = mg - F_{ext} \sin 	heta$$

Question 10

A block is pulled across a rough surface at constant speed. Which set of relationships is correct?

Accepted Answer

$$F_{ext} = f_k$$ and $$N = mg$$

Question 11

A child pushes a sled (case a) and pulls a sled (case b) with the same force $$F at $$the same angle $$	heta$$ above the horizontal. In which case is the normal force on the sled greater?

Accepted Answer

Case (a): Pushing

Question 12

Two blocks, A and B, are in contact on a frictionless air track. Block A is pushed and both blocks accelerate together. How does the net force on A compare to the net force on B?

Accepted Answer

The net force on each block is proportional to its mass

Dynamics and Forces: Newton's Laws, Friction, and Applications

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