Q: A car of mass $$1000 \ \mathrm{kg} is $$rounding a flat curve of radius $$50 \ \mathrm{m}. If $$the coefficient of static friction between the tires and the road is $$0.3$$, what is the maximum speed the car can have without skidding?

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.3 \times 9.8 \times 50} \approx 12.1 \ \mathrm{m/s}$$

Q: A 100 g ball is swung in a horizontal circle on a string that can withstand a maximum tension of $$150 \ \mathrm{N}. $$What is the maximum speed the ball can have if the radius of the circle is $$2 \ \mathrm{m}$$ before the string breaks?

$$v_{max} = \sqrt{\frac{T_{max} r}{m}} = \sqrt{\frac{150 \times 2}{0.1}} = \sqrt{3000} \approx 54.8 \ \mathrm{m/s}$$

Q: A block is placed on the outside of a frictionless sphere and released from rest at the top. At what angle from the top will the block lose contact with the sphere?

When the normal force becomes zero, which occurs at $$\theta = \cos$$^{-1}$$(2/3)$$

Question 1

Which of the following best describes why vector addition is not the same as regular addition?

Accepted Answer

Because vectors have both magnitude and direction, so their components must be added separately.

Question 2

A 0.5 kg mass is attached to a spring with a spring constant $$k = 200 \ \mathrm{N/m}$$ and is stretched $$0.1 \ \mathrm{m}$$ from equilibrium. What is the magnitude of the force exerted by the spring?

Accepted Answer

$$20 \ \mathrm{N}$$

Question 3

Which equation correctly represents Hooke's Law for the force exerted by a spring?

Accepted Answer

$$F = -k x$$

Question 4

A car of mass $$1000 \ \mathrm{kg} is $$rounding a flat curve of radius $$50 \ \mathrm{m}. If $$the coefficient of static friction between the tires and the road is $$0.3$$, what is the maximum speed the car can have without skidding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.3 	imes 9.8 	imes 50} \approx 12.1 \ \mathrm{m/s}$$

Question 5

Which of the following statements about free body diagrams is correct?

Accepted Answer

Each mass in a system has its own unique set of forces represented in its free body diagram.

Question 6

A 100 g ball is swung in a horizontal circle on a string that can withstand a maximum tension of $$150 \ \mathrm{N}. $$What is the maximum speed the ball can have if the radius of the circle is $$2 \ \mathrm{m}$$ before the string breaks?

Accepted Answer

$$v_{max} = \sqrt{\frac{T_{max} r}{m}} = \sqrt{\frac{150 	imes 2}{0.1}} = \sqrt{3000} \approx 54.8 \ \mathrm{m/s}$$

Question 7

Which of the following best describes the direction of centripetal acceleration for an object in uniform circular motion?

Accepted Answer

It always points toward the center of the circle.

Question 8

A block slides around a frictionless banked curve of radius $$r at an $$angle $$	heta. $$What is the condition for the block to move in a circle without relying on friction?

Accepted Answer

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

Question 9

Which of the following is a correct statement about the spring force in Hooke's Law?

Accepted Answer

The spring force is restorative and always acts to return the system to equilibrium.

Question 10

A mass attached to a spring oscillates with simple harmonic motion. Which of the following best describes the acceleration of the mass at maximum displacement?

Accepted Answer

The acceleration is maximum and directed toward the equilibrium position.

Question 11

A car is moving at constant speed around a circular track. Which of the following is true about its velocity and acceleration?

Accepted Answer

The speed is constant, but the velocity is changing because its direction changes; the acceleration points toward the center.

Question 12

Which of the following is the correct formula for centripetal acceleration?

Accepted Answer

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

Question 13

A block is placed on the outside of a frictionless sphere and released from rest at the top. At what angle from the top will the block lose contact with the sphere?

Accepted Answer

When the normal force becomes zero, which occurs at $$	heta = \cos$$^{-1}$$(2/3)$$

Question 14

Which of the following is a real-world example of a simple harmonic oscillator?

Accepted Answer

A mass attached to a spring oscillating back and forth.

Question 15

If a spring is stretched beyond its elastic limit, which of the following statements is true?

Accepted Answer

The spring will no longer obey Hooke's Law and may not return to its original length.

Question 16

A 2 kg object is attached to a spring and oscillates with a period of $$T = 2 \ \mathrm{s}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{4 \pi^2$ m}{T^2$} = \frac{4 \pi^2$ 	imes 2}{4} = 2 \pi^2$ \approx 19.74 \ \mathrm{N/m}$$

Question 17

Which of the following best explains why static friction is necessary for a car to round a flat curve?

Accepted Answer

Static friction provides the centripetal force required to keep the car moving in a circle.

Springs, Circular Motion, and Banked Curve Problems – Physics I Study Notes

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