Ch. 8 physics

Consider a force F=80N applied to a beam as shown in the figure below. The length of the beam is ℓ=5.0m, and θ=37∘, so that x=3.0m and y=4.0m. Of the following expressions, which ones give the correct torque produced by the force F around point P? (80 N)(3.0 m). (80 N)(5.0 m). (80 N)(4.0 m). 80 N . (48 N)(5.0 m)(sin 37∘). (80 N)(5.0 m)(sin 37∘)). (48 N)(5.0 m).

(80 N)(3.0 m). (80 N)(5.0 m)(sin 37∘)). (48 N)(5.0 m).

A solid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. It is open and at rest. A small 500-g ball is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. The ball rebounds with a speed of 16.0 m/s along the same line. What is the angular speed of the door just after the collision with the ball? 2.28 rad/s 4.57 rad/s 0.925 rad/s 1.14 rad/s 0.127 rad/s

1.14 rad/s

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg • m2 and a radius of 12.5 cm. A mass of 423 g is attached to the free end of the string. With the string vertical and taut, the mass is gently released so it can descend under the influence of gravity. As the mass descends, the string unwinds and causes the pulley to rotate, but does not slip on the pulley. What is the speed of the mass after it has fallen through 1.25 m? 2.28 m/s 2.00 m/s 1.97 m/s 4.95 m/s 3.94 m/s

1.97 m/s

Initially, a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface, as shown in the figure. The initial tangential speed of the rock was 5.0 m/s. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.25 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m? 15 m/s 9.3 m/s 3.9 m/s 75 m/s 225 m/s

15 m/s

A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal. What is the speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp? 2.2 m/s 4.0 m/s 1.9 m/s 3.5 m/s 8.0 m/s

3.5 m/s

A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill, starting from rest. If the angular speed of the disk is 4.27 rad/s at the bottom, how high did it start on the hill? 3.57 m 2.68 m 3.14 m 4.28 m

3.57m

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N • m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force? 30° 36° 24° 42°

30

The torque required to turn the crank on an ice cream maker is 4.50 N • m. How much work does it take to turn the crank through 300 full turns? 4240 J 2120 J 2700 J 1350 J 8480 J

8480 J

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s? 66.8 rad 948 rad 697 rad 83.2 rad 316 rad

948 rad

Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy? - Rotational kinetic energy is larger. - Translational kinetic energy is larger. - Both are equal. - You need to know the speed of the hoop to tell.

Both are equal

A 60-kg woman stands on the very end of a uniform board, of length ℓ, which is supported one-quarter of the way from one end and is balanced (Figure 1). 15 kg. 20 kg. 30 kg. 60 kg. 120 kg.

FN(l/4)-Mg(l/4)-60g(l/4)=0 Mg(1/4)=60g(1/4) M=60

A heavy ball suspended by a cable is pulled to the side by a horizontal force F⃗ as shown in (Figure 1). If angle is small, the magnitude of the force can be less than the weight of the ball because: - F⃗ is equal to only the x component of the tension in the cable. - even though the ball is stationary, it is not really in equilibrium. - the force holds up only part of the ball's weight. - the original statement is not true. To move the ball, F⃗ must be at least equal to the ball's weight.

F⃗ is equal to only the x component of the tension in the cable.

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.) - Her kinetic energy remains constant. - She is subject to a constant non-zero torque. - Her angular momentum remains constant. - Her moment of inertia remains constant.

Her angular momentum remains constant.

Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at 8.94 rad/s, but the other one rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system. 940 kg • m2/s 1020 kg • m2/s 975 kg • m2/s 1500 kg • m2/s

I = 1/2 Mr^2 = (.5)(65)(1.47^2) = 70.23 L = I (2(w1)-w2) = 70.23 [2(9.34) - 3.42)] = 1020 kg • m2/s

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg • m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each of mass 60 kg, are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground. What is the angular speed of the merry-go-round right after the two people have stepped on? 0.80 rad/s 0.60 rad/s 0.40 rad/s 0.20 rad/s 0.67 rad/s

I1 = 2000, w1 = 1.0 I2 = 2000 + 2 people (mr^2) I2 = 2000 + 60(5^2) + 60(5^2) I2 = 5000 (I1)(w1) = (I2)(w2) (2000)(1) = (5000)(w2) w2 = 0.4 rad/s

As you increase the force that you apply while pulling on a rope, which of the following is NOT affected? - The stress on the rope. - The Young's modulus of the rope. - The strain on the rope. - All of the above. - None of the above.

The Young's modulus of the rope.

A force of 16.88N is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel? 7.17 kg • m2 5.98 kg • m2 3.59 kg • m2 4.78 kg • m2

Torque = I(angular acceleration) Torque = Force(radius) thus I = Force(radius) / (angular acceleration) I = 16.88(0.34) / 1.2 I = 4.78 kg • m2

The drum shown in the figure has a radius of 0.40 m and a moment of inertia of 2.3 kg • m2about an axis perpendicular to it through its center. The frictional torque at the drum axle is 3.0 N • m. A 14-m length of rope is wound around the rim. The drum is initially at rest. A constant force is applied to the free end of the rope until the rope is completely unwound and slips off. At that instant, the angular speed of the drum is The drum then slows down at a constant rate and comes to a halt. In this situation, what was the magnitude of the constant force applied to the rope? 7.5 N 40 N 29 N 18 N 51 N

Torque = inertia (angular acceleration) Torque = Force(radius) Force(radius) = Inertia(angular acc) + Friction angular acc = (wf^2 - wi^2) / 2(l/r) = 7.56 rad F(0.4) = (2.3)(7.56) + 3Nm F = 51N

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest? 10 rad 13 rad 7.5 rad 5.0 rad

angular acc = (F1r1 - F2r2) t^2 / 2(m)(r^2) = [(5)(1) - (6)(0.5)] (5^2) / 2 (10) (0.5) = 5 rad

A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is - equal to the total kinetic energy of the cylinder. - more than the total kinetic energy of the cylinder. - less than the total kinetic energy of the cylinder.

less than the total kinetic energy of the cylinder.

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is - lower than when it was released. - higher than when it was released. - at the same height from which it was released. - It is impossible to tell without knowing the mass of the ball. - It is impossible to tell without knowing the radius of the ball.

lower than when it was released.

A woman is balancing on a high wire which is tightly strung, as shown in (Figure 1). The tension in the wire is The tension in the wire is: - about half the woman's weight. - about twice the woman's weight. - much less than the woman's weight. - about equal to the woman's weight. - much more than the woman's weight.

much more than the woman's weight.

A uniform beam is hinged at one end and held in a horizontal position by a cable, as shown in (Figure 1). The tension in the cable: - must be at least half the weight of the beam, no matter what the angle of the cable. - could be less than half the beam's weight for some angles. - will equal the beam's weight for all angles. - will be half the beam's weight for all angles.

must be at least half the weight of the beam, no matter what the angle of the cable.

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The LINEAR velocity of the sphere at the bottom of the incline depends on - the mass of the sphere. - the radius of the sphere. -both the mass and the radius of the sphere. - neither the mass nor the radius of the sphere.

neither the mass nor the radius of the sphere.

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, and call tL the time taken by the block on the left and tR the time taken by the block on the right to reach the bottom, respectively, then tL > tR. tL < tR. tL = tR.

tL > tR the block at the right lands first

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The ANGULAR velocity of the sphere at the bottom of the incline depends on - the mass of the sphere. - the radius of the sphere. - both the mass and the radius of the sphere. - neither the mass nor the radius of the sphere.

the radius of the sphere.