Q: A 1.00-kg object A is connected to a 2.00-kg object B, which is connected by a string over a massless, frictionless pulley to a 3.00-kg object C. Objects A and B are on a frictionless 30° incline. What is the acceleration of the system?

$$a = \dfrac{m_Cg - (m_A + m_B)g\sin\theta}{m_A + m_B + m_C}$$

Question 1

A box A weighing 80 N rests on a table. Box B is connected to box A by a rope over a frictionless, massless pulley and hangs freely. If box B weighs 70 N, what is the force exerted by the table on box A?

Accepted Answer

$$10\ \mathrm{N}$$

Question 2

In the stage set problem, a 100 kg stagehand and a 200 kg set are connected by a massless rope over a frictionless pulley. What is the acceleration of the stagehand when the rope is untied and both objects are free to move?

Accepted Answer

$$a = \dfrac{m_s - m_M}{m_s + m_M}g$$

Question 3

A 1.00-kg object A is connected to a 2.00-kg object B, which is connected by a string over a massless, frictionless pulley to a 3.00-kg object C. Objects A and B are on a frictionless 30° incline. What is the acceleration of the system?

Accepted Answer

$$a = \dfrac{m_Cg - (m_A + m_B)g\sin	heta}{m_A + m_B + m_C}$$

Question 4

A circular saw blade has a diameter of 0.25 m and spins at 3600 rpm. What is the speed of a tooth at the edge of the blade?

Accepted Answer

$$v = 2\pi f r$$

Question 5

What is the centripetal acceleration of a point on the edge of a circular saw blade of radius $$r$$ rotating at frequency $$f$$?

Accepted Answer

$$a = 4\pi^2$ f^2$ r$$

Question 6

A car of mass $$m$$ moves at constant speed $$v$$ through a dip in the road shaped as a circular arc of radius $$r. $$What is the normal force exerted by the road on the car at the bottom of the dip?

Accepted Answer

$$N = mg + \dfrac{mv^2$}{r}$$

Question 7

On a flat, unbanked road, what force provides the necessary centripetal acceleration for a car to turn a corner?

Accepted Answer

Static friction between the tires and the road

Question 8

What is the maximum speed $$v_{max} at $$which a car of mass $$m$$ can round a curve of radius $$r on a $$flat road with coefficient of static friction $$\mu$$?

Accepted Answer

$$v_{max} = \sqrt{\mu g r}$$

Question 9

A car of mass $$m$$ rounds a banked curve of radius $$r at $$angle $$	heta$$ with no friction. What speed allows the car to make the turn without sliding?

Accepted Answer

$$v = \sqrt{r g 	an 	heta}$$

Question 10

At the top of a roller coaster loop of radius $$r$$, what is the minimum speed required for the car to maintain contact with the track?

Accepted Answer

$$v_{critical} = \sqrt{g r}$$

Question 11

Two spheres exert a gravitational force of $$F$$ when separated by distance $$r. $$What is the force when the distance is halved?

Accepted Answer

$$4F$$

Question 12

According to Newton's law of gravitation, what is the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by distance $$r$$?

Accepted Answer

$$F = G \dfrac{m_1$ m_2$}{r^2$}$$

Question 13

If the gravitational force between two asteroids is $$1,000,000 N$$, what will the force be if the distance between them is doubled?

Accepted Answer

$$250,000\ \mathrm{N}$$

Question 14

What is the acceleration due to gravity $$g at $$the surface of a planet of mass $$M$$ and radius $$R$$?

Accepted Answer

$$g = \dfrac{GM}{R^2$}$$

Question 15

Two satellites of different masses orbit the Earth at the same radius. Which has the higher speed?

Accepted Answer

They have the same speed

Question 16

Identical satellites orbit at different radii. Which has the higher speed?

Accepted Answer

The one in the smaller orbit

Question 17

A satellite is boosted into a higher orbit around Earth. Which quantity increases?

Accepted Answer

Period

Question 18

What is the orbital speed $$v_{orb} of a $$satellite in a circular orbit of radius $$r$$ around a planet of mass $$M$$?

Accepted Answer

$$v_{orb} = \sqrt{\dfrac{GM}{r}}$$

Ropes and Pulleys: Forces and Accelerations in Connected Systems

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