Q: A car of mass $$m$$ drives around a flat circular track of radius $$r at $$constant speed $$v. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed the car can have without sliding off the track?

$$v_{\text{max}} = \sqrt{\mu_s g r}$$

Q: On a frictionless banked curve of radius $$r$$, what is the correct banking angle $$\theta$$ for cars to safely travel at speed $$v$$?

$$\tan \theta = \frac{v^2$}{r g}$$

Question 1

Which of the following correctly expresses the x-component of acceleration for a projectile subject to aerodynamic drag, according to the drag model shown in the study materials?

Accepted Answer

$$a_x = -\frac{\rho C A}{2m} v_x \sqrt{v_x^2$ + v_y^2$}$$

Question 2

A rocket-powered hockey puck of mass $$0.50\ \mathrm{kg} is $$released from rest on a frictionless table with a thrust of $$2.0\ \mathrm{N}$$, $$4.0\ \mathrm{m}$$ from the edge, which drops $$2.0\ \mathrm{m}$$ vertically. Neglecting air resistance, how far from the base of the table does the puck land?

Accepted Answer

$$5.7\ \mathrm{m}$$

Question 3

In the absence of air drag, what launch angle maximizes the range of a projectile that lands at the same elevation from which it was launched?

Accepted Answer

$$45^\circ$$

Question 4

For an object in uniform circular motion (UCM) of radius $$r$$ and speed $$v$$, what is the magnitude of the radial (centripetal) acceleration?

Accepted Answer

$$a_r = \frac{v^2$}{r}$$

Question 5

A car of mass $$m$$ drives around a flat circular track of radius $$r at $$constant speed $$v. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed the car can have without sliding off the track?

Accepted Answer

$$v_{	ext{max}} = \sqrt{\mu_s g r}$$

Question 6

On a frictionless banked curve of radius $$r$$, what is the correct banking angle $$	heta$$ for cars to safely travel at speed $$v$$?

Accepted Answer

$$	an 	heta = \frac{v^2$}{r g}$$

Question 7

A projectile is launched with initial speed $$v_0 at $$angle $$	heta$$ into a headwind that exerts a constant horizontal drag force $$F_w = -F_w \hat{i}. $$Which of the following best describes the effect of the headwind on the projectile's range?

Accepted Answer

The range decreases compared to no wind.

Question 8

Which of the following is NOT a valid assumption for solving the rocket-powered hockey puck problem described in the study materials?

Accepted Answer

The puck rotates so that the thrust direction changes during motion.

Question 9

For a car going around a banked curve with both friction and banking present, which forces contribute to the centripetal force required for circular motion?

Accepted Answer

The r-components of both the normal force and static friction.

Question 10

Given the kinematic equation for constant acceleration in the x-direction: $$x_f = x_i + v_{x,i} \Delta t + \frac{1}{2} a_x (\Delta t)^2$, which variable must be known to solve for x_f$ if all others are given?

Accepted Answer

$$v_{x,i}$$

Question 11

A soccer ball is kicked with spin, causing it to curve in flight. What physical effect is primarily responsible for this sideways force?

Accepted Answer

The Magnus effect due to pressure differences created by spin.

Question 12

Which equation correctly relates the y-component of velocity for constant acceleration?

Accepted Answer

$$v_{y,f} = v_{y,i} + a_y \Delta t$$

Question 13

A golf ball is hit with initial velocity $$v_0 at an $$angle $$	heta in $$the presence of air drag. Compared to the ideal case (no drag), what happens to the maximum height and range?

Accepted Answer

Both maximum height and range decrease.

Question 14

In uniform circular motion, what is the direction of the net force acting on the object?

Accepted Answer

Always toward the center of the circle (radially inward).

Question 15

A car of mass $$m$$ goes around a highway curve of radius $$r$$ banked at angle $$	heta$$ with coefficient of static friction $$\mu_s. $$What is the expression for the maximum speed $$v_{	ext{max}}$$ the car can have without sliding?

Accepted Answer

$$v_{	ext{max}} = \sqrt{r g \frac{\sin 	heta + \mu_s \cos 	heta}{\cos 	heta - \mu_s \sin 	heta}}$$

Question 16

Which of the following is true about the equations for acceleration components with aerodynamic drag?

Accepted Answer

The x and y components are coupled and depend on both $$v_x$$ and $$v_y.$$

Question 17

Which of the following best describes the role of the normal force on a frictionless banked curve?

Accepted Answer

Its radial component provides the required centripetal force.

Question 18

A baseball curves in flight due to spin. Which real-world phenomenon is this most closely related to?

Accepted Answer

The Magnus effect.

Question 19

If a projectile is launched with initial velocity $$v_0 at $$angle $$	heta$$ and experiences a constant horizontal drag force $$F_w$$, which of the following is true about the optimal launch angle for maximum range?

Accepted Answer

It is less than $$45^\circ.$$

Chapter 8: 2D Dynamics – Kinematics, Dynamics, and Projectile Motion with Drag

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드