Q: A car is driving on a highway curve that is banked at an angle $$\theta. If $$the car's speed is $$v$$ and the radius of the curve is $$r$$, what is the correct expression for the banking angle $$\theta$$ that allows the car to make the turn without relying on friction?

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

Q: An object of mass $$m_1$$ hangs vertically from a pulley at the top of a frictionless ramp inclined at angle $$\theta. $$Another object of mass $$m_2$$ rests on the ramp, attached to the same rope over the pulley. What is the acceleration $$a of $$the system?

$$a = \dfrac{m_1$ g - m_2$ g \sin \theta}{m_1$ + m_2$}$$

Q: A projectile is launched with initial velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the maximum range $$R of $$the projectile (assuming it lands at the same height it was launched)?

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

Q: A car of mass $$m is $$moving at speed $$v$$ around a banked curve of radius $$r$$ with banking angle $$\theta. If $$the friction is negligible, what is the normal force $$N$$ acting on the car?

$$N = m g / (\cos \theta + \sin \theta \dfrac{v^2$}{g r})$$

Q: A projectile is launched at an angle $$\theta$$ with initial velocity $$v_0. $$What is the time of flight $$T if it $$lands at the same height it was launched?

$$T = \dfrac{2 v_0$ \sin \theta}{g}$$

Question 1

A car is driving on a highway curve that is banked at an angle $$	heta. If $$the car's speed is $$v$$ and the radius of the curve is $$r$$, what is the correct expression for the banking angle $$	heta$$ that allows the car to make the turn without relying on friction?

Accepted Answer

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

Question 2

An object of mass $$m_1$$ hangs vertically from a pulley at the top of a frictionless ramp inclined at angle $$	heta. $$Another object of mass $$m_2$$ rests on the ramp, attached to the same rope over the pulley. What is the acceleration $$a of $$the system?

Accepted Answer

$$a = \dfrac{m_1$ g - m_2$ g \sin 	heta}{m_1$ + m_2$}$$

Question 3

A student stands on top of a building of height $$h$$ and throws a ball horizontally with initial velocity $$v_0. $$Where does the ball land relative to the base of the building?

Accepted Answer

$$x = v_0$ \sqrt{\dfrac{2h}{g}}$$

Question 4

A car of mass $$m$$ travels at velocity $$v$$ around an unbanked curve of diameter $$d. $$What is the minimum frictional force required to keep the car from skidding?

Accepted Answer

$$f = \dfrac{m v^2$}{d/2}$$

Question 5

A projectile is launched with initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the maximum range $$R of $$the projectile (assuming it lands at the same height it was launched)?

Accepted Answer

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

Question 6

A block of mass $$m is on a $$frictionless table on Earth. If a force $$F is $$applied, what is its acceleration $$a$$? If the same force is applied to the block on the Moon, where gravity is $$g_{moon}$$, what is the acceleration?

Accepted Answer

On both Earth and Moon, $$a = \dfrac{F}{m}$$

Question 7

You are standing on Earth and experience a gravitational pull from the planet. If you are on the Moon, you also experience a pull. What is the gravitational force $$F$$ between the Earth and the Moon, given their masses $$M_{earth}$$ and $$M_{moon}$$ and the distance $$r$$ between them?

Accepted Answer

$$F = G \dfrac{M_{earth} M_{moon}}{r^2$}$$

Question 8

A car of mass $$m is $$moving at speed $$v$$ around a banked curve of radius $$r$$ with banking angle $$	heta. If $$the friction is negligible, what is the normal force $$N$$ acting on the car?

Accepted Answer

$$N = m g / (\cos 	heta + \sin 	heta \dfrac{v^2$}{g r})$$

Question 9

A ball is thrown horizontally from a building of height $$h$$ and lands a distance $$x$$ from the base. What is the initial velocity $$v_0 of $$the ball?

Accepted Answer

$$v_0$$ = \dfrac{x}{\sqrt{2h/g}}$$

Question 10

A block of mass $$m is $$pushed with force $$F on a $$frictionless table. If the same block is pushed with the same force on the Moon, where gravity is $$g_{moon}$$, which statement is true?

Accepted Answer

The acceleration is the same on Earth and Moon, $$a = \dfrac{F}{m}$$

Question 11

A car of mass $$m$$ travels at speed $$v$$ around a curve of radius $$r. $$What is the centripetal acceleration $$a_c$$?

Accepted Answer

$$a_c = \dfrac{v^2$}{r}$$

Question 12

A projectile is launched at an angle $$	heta$$ with initial velocity $$v_0. $$What is the time of flight $$T if it $$lands at the same height it was launched?

Accepted Answer

$$T = \dfrac{2 v_0$ \sin 	heta}{g}$$

Question 13

A car of mass $$m$$ moves at speed $$v$$ around a flat curve of radius $$r. $$What is the minimum coefficient of friction $$\mu$$ required to prevent skidding?

Accepted Answer

$$\mu = \dfrac{v^2$}{g r}$$

Question 14

Two objects, one of mass $$m_1$$ and the other $$m_2$$, are connected by a rope over a frictionless pulley. If $$m_1$$ \u003e $$m_2$$, what is the acceleration $$a of $$the system?

Accepted Answer

$$a = \dfrac{(m_1$ - m_2$) g}{m_1$ + m_2$}$$

Question 15

A ball is thrown horizontally from a building and lands $$x$$ meters away after $$t$$ seconds. What is the height $$h of $$the building?

Accepted Answer

$$h = \dfrac{1}{2} g t^2$

Question 16

A car of mass $$m$$ travels at speed $$v$$ around a banked curve of radius $$r$$ with banking angle $$	heta. If $$the friction is not negligible, what is the maximum speed $$v_{max}$$ the car can have without skidding up the bank?

Accepted Answer

$$v_{max} = \sqrt{r g (	an 	heta + \mu)}$$

Question 17

A block of mass $$m is $$pushed with force $$F on a $$frictionless table. If the same block is pushed with the same force on a rough table with coefficient of friction $$\mu$$, what is its acceleration $$a$$?

Accepted Answer

$$a = \dfrac{F - \mu m g}{m}$$

Question 18

A projectile is launched from the ground at an angle $$	heta$$ with initial velocity $$v_0. $$What is the maximum height $$H$$ reached by the projectile?

Accepted Answer

$$H = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Physics 1 Exam Review: Dynamics, Circular Motion, and Projectile Motion

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