PHY 221 Final

An aircraft performs a maneuver called an "aileron roll." During this maneuver, the plane turns like a screw as it maintains a straight flight path, which sets the wings in circular motion. If it takes it 35 s to complete the circle and the wingspan of the plane is 11 m, what is the acceleration of the wing tip?

0.18 m/s2

The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2?

0.41R

A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20 N/m oscillates on a horizontal, frictionless track. At time t=0.00s , the mass is released from rest at 10.0cm . (That is, the spring is stretched by 10.0 cm.)(a) Find the frequency of the oscillations.(b) Determine the maximum speed of the mass. At what point in the motion does the maximum speed occur?(c) What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur?(d) Determine the total energy of the oscillating system.(e) Express the displacement x as a function of time t.

(a) 0.58 Hz (b) 0.37 m/s, at the equilibrium position(c) 1.3 m/s2, at maximum displacement(d) 0.10 J (e) x = (0.10 m) cos(3.7t)

When a 2.75-kg fan, having blades 18.5 cm long, is turned off, its angular speed decreases uniformly from 10.0 rad/s to 6.30 rad/s in 5.00 s. (a) What is the magnitude of the angular acceleration of the fan?(b) Through what angle (in degrees) does it turn while it is slowing down during the 5.00 s?(c) If its angular acceleration does not change, how long after it is turned off does it take the fan to stop.

(a) 0.740 rad/s2 (b) 2330° (c) 13.5 s

An extremely light rod 1.00 m long has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other. The system rotates at a constant angular speed about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached. The kinetic energy of the system is measured to be 100.0 J. (a) What is the moment of inertia of this system about the fixed axis? (b) What is the angular speed (in revolutions per second) of this system?

(a) 1.25 kg • m2 (b) 2.01 rev/s

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board(a) by pillar A.(b) by pillar B.

(a) 1.71 kN downwards (b) 2.51 kN upwards

The position of an object that is oscillating on an ideal spring is given by the equation x= (12.3cm)cos((1.26s^-1)t) . At time t=0.815s ,(a) how fast is the object moving?(b) what is the magnitude of the acceleration of the object?

(a) 13.3 cm/s (b) 10.1 cm/s2

A 3.45-kg centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration. A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed.(a) What is the angular acceleration (in rad/s2) of the centrifuge as it spins up?(b) How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

(a) 18.8 rad/s2 (b) 1.49 × 104 revolutions

A satellite that weighs 4900 N on the launchpad travels around the earth's equator in a circular orbit with a period of 1.667 h. The earth's mass is 5.97 × 1024 kg, its equatorial radius is 6.3 × 106 m, and G = 6.67 × 10-11 N • m2/kg2.(a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the Earth's SURFACE.

(a) 3910 N (b) 7.55 × 105 m

A force 𝐹 = 3.00 𝑁𝑖̂ − 2.00 𝑁 𝑗̂ acts at a location 𝑟⃗ = 1.00 𝑚 𝑖̂ + 2.00 𝑚 𝑗̂ an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy- plane?

-8.00 N∙m

A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is closest to

0.0372 N ∙ m

What is the ratio of the escape speed of a rocket launched from sea level to the escape speed of one launched from Mt. Everest (an altitude of 8.85 km)? The radius of the earth is 6.38x10^6 m.

1.0007

In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg • m2 and radius 5.00 cm. The coefficient of friction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find the speed of the upper block just as it has moved 0.600 m.

1.40 m/s

A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam?

1.98 m

A very thin uniform rod, 2.40 m long and of weight 135 N, has a frictionless hinge at its lower end. It starts out vertically from rest and falls, pivoting about the hinge. Just as it has rotated through an angle of 55.0°, what is the downward acceleration of the end farthest from the hinge?

12.0 m/s^2

The components of vector B are Bx = -3.5 and By = -9.7, and the components of vector C are Cx = -6 and Cy = +8.1. What is the angle (less than 180 degrees) between vectors B and C?

124 degrees

A machinist turns the power on to a grinding wheel, which is at rest at time t=0.00s . The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 25 rad/s. The wheel is run at that angular velocity for 37 s and then power is shut off. The wheel decelerates uniformly at 1.5rad/s^2 until the wheel stops. In this situation, the time interval of angular deceleration (slowing down) is closest to

17 s

A 95 N force exerted at the end of a torque wrench gives rise to a torque of 15 Nm. What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force?

18 degrees

If the mass of the earth and all objects on it were suddenly doubled, but the size remained the same, the acceleration due to gravity at the surface would become

2 times what it now is.

A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?

2.0 kg∙m2/s towards the west

A disk-shaped space station 175 m in diameter spins uniformly about an axis perpendicular to the plane of the disk through its center. How many rpm (rev/min) must this disk make so that the acceleration of all points on its rim is g/2?

2.26 rev/min

An object of mass 8.0 kg is attached to an ideal massless spring and allowed to hang in the Earth's gravitational field. The spring stretches 3.6 cm before it reaches its equilibrium position. If this system is allowed to oscillate, what will be its frequency?

2.6 Hz

An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the spring constant of the spring?

24.1 N/m

For the vectors shown in the figure, find the magnitude and direction of B × A , assuming that the quantities shown are accurate to two significant figures.

26, directed into the plane

Two identical ladders are 3.0 m long and weigh 600 N each. They are connected by a hinge at the top and are held together by a horizontal rope, 1.0 m above the smooth floor forming a symmetric "A" arrangement. The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint. What is the tension in the rope?

280 N

A satellite in a circular orbit of radius R around planet X has an orbital period T. If Planet X had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be

2T

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal. After it has rolled 4.20 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?

3.07 m/s2

In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

35 s

As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by

35.5 N at an angle 34.3° with respect to +x-axis.

Planet Z-34 has a mass equal to 1/3 that of Earth, a radius equal to 1/3 that of Earth, and an axial spin rate 1/2 that of Earth. With g representing, as usual, the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

3g.

In the figure, a very light rope is wrapped around a wheel of radius R = 2.0 meters and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel?

53.8 kg m/s^2

In the figure, a block of mass M hangs at rest. The rope that is fastened to the wall is horizontal and has a tension off 52 N. The rope that is fastened to the ceiling has a tension of and makes an angle θ with the ceiling. What is the angle θ?

55°

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface. If this object is moved 500 km farther from the planet, the gravitational force on it will be closest to

56 N

You push downward on a box at an angle 25° below the horizontal with a force of . If the box is on a flat horizontal surface for which the coefficient of static friction with the box is 0.76, what is the mass of the heaviest box you will be able to move?

59 kg

A hobby rocket reaches a height of and lands from the launch point with no air resistance. What was the angle of launch?

69.0°

A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth?

7075 N

A satellite is in circular orbit at an altitude of 1500 km above the surface of a nonrotating planet with an orbital speed of 9.2 km/s. The minimum speed needed to escape from the surface of the planet is 14.9 km/s, and G = 6.67 × 10-11 N • m2/kg2. The orbital period of the satellite is closest to

72 min

Two stones, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these stones is true?

At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy.

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

B (pie)

If the torque on an object adds up to zero

the object could be both turning and accelerating linearly

Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Block 2 is faster.

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?

Both are equal.

In a collision between two objects having unequal masses, how does magnitude of the impulse imparted to the lighter object by the heavier one compare with the magnitude of the impulse imparted to the heavier object by the lighter one?

Both objects receive the same impulse.

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?

Both reach the bottom at the same time.

A restoring force of magnitude F acts on a system with a displacement of magnitude x. In which of the following cases will the system undergo simple harmonic motion?

F proportional to x

A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass.

False

If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest.

False

Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion?

In equal times its velocity changes by equal amounts

Consider a uniform solid sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Its translational kinetic energy is larger than its rotational kinetic energy.

Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do.

Neither of them does any work.

A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.

Nothing will happen; the seesaw will still be balanced

A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A?

T

A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth. If the satellite instead had mass 4m, its orbital period would be

T

An object is executing simple harmonic motion. What is true about the acceleration of this object? (There may be more than one correct choice.)

The acceleration is a maximum when the object is instantaneously at rest. The acceleration is zero when the speed of the object is a maximum. The acceleration is a maximum when the displacement of the object is a maximum.

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation. If you release the hanging blocks simultaneously from rest, and if the ropes do not slip, which block lands first?

The block at the right lands first (closer to axis)

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no slipping?

The disk

A baseball is located at the surface of the earth. Which statements about it are correct? (There may be more than one correct choice.)

The gravitational force on the ball due to the earth is exactly the same as the gravitational force on the earth due to the ball.

A constant force acts on a moving object. The object makes a fixed magnitude of displacement in some direction. In general, in what direction is the displacement that will result in the object traveling with the least kinetic energy after the displacement occurs?

The opposite direction as the force

A small car has a head-on collision with a large truck. Which of the following statements concerning the magnitude of the average force due to the collision is correct?

The small car and the truck experience the same average force.

Two objects are thrown from the top of a tall building and experience no appreciable air resistance. One is thrown up, and the other is thrown down, both with the same initial speed. What are their speeds when they hit the street?

They are traveling at the same speed.

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?

They both slide to the same height.

A satellite is orbiting the earth. If a payload of material is added until it doubles the satellite's mass, the earth's pull of gravity on this satellite will double but the satellite's orbit will not be affected.

True

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.

True

Consider what happens when you jump up in the air. Which of the following is the most accurate statement?

When you push down on the earth with a force greater than your weight, the earth will push back with the same magnitude force and thus propel you into the air.

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz.(a) What is the maximum speed of the needle?(b) What is the maximum acceleration of the needle?

a) 0.2 m/s at equilibrium b) 3.26 m/s^2 at turning point

The position of an object that is oscillating on an ideal spring is given by the equation . At time , (a) how fast is the object moving?(b) what is the magnitude of the acceleration of the object?

a) 13.3 cm/s b) 10.1 cm/s^2

An object weighing 44.1 N hangs from a vertical massless ideal spring. When set in vertical motion, the object obeys the equation y (t) = (6.20 cm) cos [(2.74 rad/s) t - 1.40].(a) Find the time for this object to vibrate one complete cycle.(b) What are the maximum speed and maximum acceleration of the object? (c) What is the TOTAL distance the object moves through in one cycle. (d) Find the maximum kinetic energy of the object.(e) What is the spring constant of the spring.

a) 2.29s b) 0.17 m/s c) 0.248m d) 0.065J e) 33.8 N/m

A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above the horizontal. The speed of the ball at the base of the ramp is 2.63 m/s. While the ball is moving up the ramp, find(a) the acceleration (magnitude and direction) of its center of mass and (b) the friction force (magnitude and direction) acting on it due to the surface of the ramp.

a) 2.94 m/s^2 b) 3.43 N up the ramp

A 12.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by . (a) What is the spring constant of the spring?(b) What is the maximum acceleration of the object?(c) What is the maximum speed that the object reaches?(d) How long does it take the object to go from its highest point to its lowest point?

a) 456.6 N/m b) 17.1 m/s^2 c) 0.878 m/s d) 0.16 s

When a rigid body rotates about a fixed axis, all the points in the body have the same

angular acceleration

A 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 as shown in the figure. When the ball reaches its maximum height on the frictionless surface, it is

at a lesser height than when it was released.

If we double only the mass of a vibrating ideal mass-and-spring system, the mechanical energy of the system

does not change

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

down

If we double only the spring constant of a vibrating ideal mass-and-spring system, the mechanical energy of the system

increases by a factor of 2.

An object is moving to the right, and experiencing a net force that is directed to the right. The magnitude of the force is decreasing with time. The speed of the object is

increasing.

A baseball is thrown vertically upward and feels no air resistance. As it is rising

its momentum is not conserved, but its mechanical energy is conserved.

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

solid sphere

A uniform disk, a uniform hoop, and a uniform solid sphere are released at the same time at the top of an inclined ramp. They all roll without slipping. In what order do they reach the bottom of the ramp?

sphere, disk, hoop

A mass M is attached to an ideal massless spring. When this system is set in motion, it has a period T. What is the period if the mass is doubled to 2M?

sqrt(2)T

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. During this collision

the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.

A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car. During the collision

the force of on the truck due to the collision is exactly equal to the force on the car.

The angular momentum of a system remains constant

when no torque acts on the system

A machine part is vibrating along the x-axis in simple harmonic motion with a period of 0.27s and a range (from the maximum in one direction to the maximum in the other) of 3cm. At time t = 0 it is at its central position and moving in the +x direction. What is its position when t=55?

x = -1.4 cm

A certain planet has an escape speed V. If another planet of the same size has twice the mass as the first planet, its escape speed will be

√2V