Q: A 1500 kg car is making a left turn on a flat, unbanked road with a radius of 25 m. If the coefficient of static friction between the tires and the road is 0.8, what is the maximum speed at which the car can make the turn without sliding?

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.8 \times 9.8 \times 25} \approx 14 m/s$$

Q: A child of mass 20 kg sits on a 5 kg cart. The cart is spun in a circle of radius 2 m by a rope with a tension of 100 N. What is the number of revolutions per minute (rpm) the cart makes?

$$\omega = \sqrt{\frac{T}{m r}} = \sqrt{\frac{100}{25 \times 2}} = \sqrt{2} \approx 1.41$$ \text{ rad/s}; \text{rpm} = \frac{1.41 \times 60}{2\pi} \approx 13.5$

Q: A car of mass 1200 kg is moving at 20 m/s around a flat curve of radius 40 m. What is the required frictional force to keep the car from sliding?

$$F_{friction} = \frac{m v^2$}{r} = \frac{1200 \times 20^2$}{40} = 12,000 N$$

Q: A 2 kg object moves in a circle of radius 0.5 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

$$F_c = \frac{m v^2$}{r} = \frac{2 \times 16}{0.5} = 64 N$$

Q: A car drives around a flat, 50-m-diameter track, applying a steady 500 N forward force. If the coefficient of static friction is 0.4, what is the maximum speed before the car slides out of the curve?

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.4 \times 9.8 \times 25} \approx 9.9 m/s$$

Question 1

A 1500 kg car is making a left turn on a flat, unbanked road with a radius of 25 m. If the coefficient of static friction between the tires and the road is 0.8, what is the maximum speed at which the car can make the turn without sliding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.8 	imes 9.8 	imes 25} \approx 14 m/s$$

Question 2

A child of mass 20 kg sits on a 5 kg cart. The cart is spun in a circle of radius 2 m by a rope with a tension of 100 N. What is the number of revolutions per minute (rpm) the cart makes?

Accepted Answer

$$\omega = \sqrt{\frac{T}{m r}} = \sqrt{\frac{100}{25 	imes 2}} = \sqrt{2} \approx 1.41$$ 	ext{ rad/s}; 	ext{rpm} = \frac{1.41 	imes 60}{2\pi} \approx 13.5$

Question 3

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

Accepted Answer

It points toward the center of the circle.

Question 4

A rollercoaster car of mass $$m$$ goes over the top of a loop of radius $$r. $$What is the minimum speed $$v_c at $$the top required for the car to stay on the track?

Accepted Answer

$$v_c = \sqrt{g r}$$

Question 5

A satellite orbits a planet at a distance $$r$$ from the planet's center. What is the orbital speed $$v_{orbit}$$ required for a circular orbit near the planet's surface, assuming gravitational acceleration $$g$$?

Accepted Answer

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

Question 6

A car of mass $$m$$ drives around a banked curve of radius $$r at $$speed $$v. If $$the banking angle is $$	heta$$ and friction is negligible, what is the optimal speed for the car to take the curve without sliding?

Accepted Answer

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

Question 7

Which statement about centrifugal force is correct?

Accepted Answer

It is a fictitious force that appears in non-inertial (accelerating) reference frames.

Question 8

A ball is swung in a horizontal circle on a string. If the string breaks, what path will the ball follow immediately after?

Accepted Answer

It will move in a straight line tangent to the circle at the point of release.

Question 9

A car of mass 1200 kg is moving at 20 m/s around a flat curve of radius 40 m. What is the required frictional force to keep the car from sliding?

Accepted Answer

$$F_{friction} = \frac{m v^2$}{r} = \frac{1200 	imes 20^2$}{40} = 12,000 N$$

Question 10

A person in an elevator feels 'weightless' when the elevator is in free fall. What is their apparent weight?

Accepted Answer

$$W_{apparent} = 0$$

Question 11

A 2 kg object moves in a circle of radius 0.5 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$F_c = \frac{m v^2$}{r} = \frac{2 	imes 16}{0.5} = 64 N$$

Question 12

Which of the following is true about the forces acting on a rollercoaster car at the top of a vertical loop?

Accepted Answer

Both gravity and the normal force point toward the center of the loop.

Question 13

A car drives around a flat, 50-m-diameter track, applying a steady 500 N forward force. If the coefficient of static friction is 0.4, what is the maximum speed before the car slides out of the curve?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.4 	imes 9.8 	imes 25} \approx 9.9 m/s$$

Question 14

Which of the following is NOT a step in the Newtonian mechanics problem-solving strategy?

Accepted Answer

Assume the object is in equilibrium regardless of the situation.

Question 15

A particle moves in a circle of radius $$r$$ with angular speed $$\omega. $$What is its tangential velocity?

Accepted Answer

$$v = \omega r$$

Question 16

A satellite in orbit around Earth at radius $$r$$ has a period $$T. $$Which formula gives the period in terms of orbital speed $$v_{orbit}$$?

Accepted Answer

$$T = \frac{2 \pi r}{v_{orbit}}$$

Question 17

Which of the following statements about reference frames is correct?

Accepted Answer

Newton's laws are only valid in inertial reference frames.

Question 18

A person riding in a car feels pushed against the door when the car turns left. What is the actual force acting on the person?

Accepted Answer

The normal force from the door pushes the person toward the center of the curve.

Dynamics II: Motion in a Plane and Circular Motion

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