(AP CM) Quiz 3.1

A ball of mass 0.40 kg is attached to a light rope of length 1.0 m. The ball is moving in a vertical circle, as shown in the figure, with Earth's gravitational force as the only force external to the ball-string system. The speed of the ball at point P is 5.4 m/s. The centripetal acceleration of the ball at point P is most nearly

• 5.4 m/s

• 9.8 m/s

• 29.2 m/s

• 39.2 m/s

Car A can travel around a curved section of road without skidding at a maximum constant speed of 10 m/s. When car B travels around the same curve without skidding at its maximum speed, it has 1/4 the centripetal acceleration as car A. The maximum speed at which car B can safely travel around the curve is most nearly

• 5.0 m/s

• 10 m/s

• 14 m/s

• 20 m/s

A cart of mass M is approaching a hill with a circular top of radius R as shown in the figure. The cart is carrying a load also of mass M and is traveling with speed  $v_0$  when it is at the top of the hill. The length of the cart is negligible in comparison to the radius of the hill. The cart never loses contact with the hill's surface. The cart and load can both be considered to be at the same position.

The speed  $v_{\min}$  is the minimum speed necessary for the cart and the load to leave the surface of the hill at the top of the hill. If the load is removed, what is the new minimum speed necessary for the cart to leave the surface of the hill?

•  $\frac{1}{4}v_{\min}$  

•  $\frac{1}{2}v_{\min}$  

•  $v_{\min}$  

•  $2v_{\min}$  

One end of a string is fixed. An object attached to the other end moves on a horizontal plane with uniform circular motion of radius R and frequency f. The tension in the string is  $F_S$  . If both the radius and frequency are doubled, the tension is

•  $\frac{1}{2}F_S$  

•  $2F_S$  

•  $4F_S$  

•  $8F_S$  

A physics student attempts to plot the acceleration of a track runner that runs counterclockwise at constant speed around the path shown. THe path is such that the lengths of its segments, PQ, QR, RS, and SP, are equal. Arcs QR and SP are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time t during one trip around the path, beginning at point P?

• 
• 
• 
• 

On a level horizontal table, a toy race car of mass M moves with constant speed v around a flat circular racetrack of radius R, as shown in the left figure. The toy car is now going around a banked curve, shown in the right figure. The banked curve is higher toward the outside of the circular turn. The toy car can now travel at a higher speed without sliding because the banked curve.

• increases the coefficient of friction between the car and the track

• allows a component of the normal force to point toward the center of the track

• Allows a component of the weight of the car to point toward the center of the track

• allows gravity to do work on the car

On a level horizontal table, a toy race car of mass M moves with constant speed v around a flat circular racetrack of radius R. Which of the following best represents the minimum coefficient of static friction required for the race car to continue to follow the circular path shown?

• $M\frac{v^2}{R}$

• $\frac{v^2}{g}$

• $\frac{v^2}{Rg}$

• $\frac{v^2}{2Rg}$

The maximum mass that can be hung vertically from a string without breaking the string is 10 kg. A length of this string that is 2 m long is used to rotate a 0.5 kg object in a circle on a frictionless table with the string horizontal. The maximum speed that the mass can attain under these conditions without the string breaking is most nearly

• 10 m/s

• 14 m/s

• 20 m/s

• 100 m/s

A particle of mass m moves counterclockwise around a horizontal circle of radius r, as shown in the figure. The speed of the particle is given as a function of time t by  $v\left(t\right)=bt$  , where b is a positive constant and  $t\ge0$  . Which of the following best describes the acceleration vector for the particle at the moment shown in the diagram

• It is directed toward the bottom of the image

• It is directed toward the top of the image

• It has components directed toward the right and toward the bottom of the image

• It has components directed toward the left and toward the bottom of the image.

A car of mass M is traveling over a hill that has a radius of curvature R. The car is slowing down such that its tangential acceleration is  $a_T$  . The net acceleration of the car at the top of the hill is best described by 

•  $a_C$   

•  $a_T$ 

•  $a_C+a_T$  

•  $\sqrt{a_C^2+a_T^2}$