Q: A car of mass $$m$$ moves at speed $$v$$ around a banked curve of radius $$r$$ with no friction. What is the banking angle $$\theta$$ required for no friction? Use $$\tan \theta = \frac{v^2$}{rg}.$$

$$\tan \theta = \frac{v^2$}{rg}$$

Question 1

A 10.0 kg object is acted upon by the forces shown in the diagram (see $$image_1). $$What is the x-component of the object's acceleration $$a_x (in m/s$^2$$)? Use $$\sum F_x = m a_x.$$

Accepted Answer

$$a_x = 0.25$$

Question 2

Given the same force diagram (see $$image_1$$), what is the y-component of the object's acceleration $$a_y (in m/s$^2$$)? Use $$\sum F_y = m a_y.$$

Accepted Answer

$$a_y = 0.5$$

Question 3

Two friends slide a 175 kg box across the floor. One pushes with 225 N and the other pulls with 310 N. The box moves at constant speed. What is the coefficient of kinetic friction $$\mu_k$$? (Use $$f_k = \mu_k N$$ and $$N = mg.)$$

Accepted Answer

$$\mu_k = 0.32$$

Question 4

A cart of mass $$m is at $$rest. A force $$F is $$applied for time $$\Delta t$$, giving it speed $$v. If $$the same force is applied for the same time to a cart of mass $$4m$$, what is its final speed?

Accepted Answer

$$\frac{1}{2}v$$

Question 5

Refer to the pulley system (see $$image_3). $$Both masses are 5 kg and the pulleys are frictionless. What does the spring scale read?

Accepted Answer

5 kg

Question 6

A car turns a corner on a banked road. Which free-body diagram (see $$image_4) $$correctly represents the forces acting on the car?

Accepted Answer

Diagram B

Question 7

A block on a string spins in a horizontal circle on a frictionless table counterclockwise. The block is held by the tension of the string (TA to TD). Which is correct?

Accepted Answer

TA = TC \u003e TD \u003e TB

Question 8

An object in a circular orbit near the surface of a planet (gravity $$g = 6.7 m/s$^2$$, radius $$r = 9,800 km) is $$experiencing uniform circular motion. What is its orbital velocity $$v$$? Use $$v = \sqrt{g r}.$$

Accepted Answer

$$v = 8 km/s$$

Question 9

A mosquito runs head-on into a truck. Which is true during the collision?

Accepted Answer

The mosquito exerts the same force on the truck as the truck exerts on the mosquito.

Question 10

A 1600 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of the friction force on the car? (Use $$f = m \frac{v^2$}{r}.)$$

Accepted Answer

$$7200 N$$

Question 11

A space station is constructed as a 1200-m-diameter cylinder that rotates about its axis. What rotation period will provide 'normal' gravity ($$g = 9.8 m/s$^2$$)? Use $$T = 2\pi \sqrt{\frac{r}{g}}$$ with $$r = 600 m.$$

Accepted Answer

$$49 s$$

Question 12

A 5.0 N force acts at $$20^\circ$$ below the x-axis. What is the x-component of this force? Use $$F_x = F \cos 	heta.$$

Accepted Answer

$$4.7 N$$

Question 13

A 5.0 N force acts at $$20^\circ$$ below the x-axis. What is the y-component of this force? Use $$F_y = F \sin 	heta.$$

Accepted Answer

$$-1.7 N$$

Question 14

A 2.82 N force acts along the positive y-axis. What is the acceleration of a 10 kg object due to this force? Use $$a = F/m.$$

Accepted Answer

$$0.282$$ 	ext{ m/s}^2$

Question 15

A block is spun in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the direction of the net force acting on the block?

Accepted Answer

Toward the center of the circle

Question 16

A car of mass $$m$$ moves at speed $$v$$ around a banked curve of radius $$r$$ with no friction. What is the banking angle $$	heta$$ required for no friction? Use $$	an 	heta = \frac{v^2$}{rg}.$$

Accepted Answer

$$	an 	heta = \frac{v^2$}{rg}$$

Physics with Calculus: Forces, Motion, and Circular Dynamics – Guided Study Notes

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