Physics Midterm

If a tree is 15 m tall, its height expressed in feet is x ft, where x is

greater than 15.

In the figure, a 60-cm length of uniform wire, of 60 g mass and negligible thickness, is bent into a right triangle. The x and y coordinates of the center of mass, in cm, are closest to

(10,3)

A 500-g particle is located at the point r =4mi^+3mj^−2mk and is moving with a velocity v=5m/si^−2m/sj^+4m/sk. What is the angular momentum of this particle about the origin?

(4i-13j-11.5k) kg*m^2/s

What is the torque about the origin on a particle located at r=3mi+4mj−2mk if a fore F→=5Ni−2Nj+3Nk acts on the particle?

(8i-19j-26k)

Three cars (car F, car G, and car H) are moving with the same velocity when the driver suddenly slams on the brakes, locking the wheels. The most massive car is car F, the least massive is car H, and all three cars have identical tires. (a) Which car travels the longest distance to skid to a stop? b) For which car does friction do the largest amount of work in stopping the car?

(a) they all travel at the same distance in stopping (b)car F

A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle. The pulley is initially not turning. A constant force of 50 N is applied to the string, which does not slip, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

0.20 kg.m^2

Under what condition is |A→−B→|=A+B?

-The magnitude of vector B is zero. -Vectors A and B are in opposite directions.

Two ice skaters push off against one another starting from a stationary position. The 45.0-kg skater acquires a speed of 0.375 m/s. What speed does the 60.0-kg skater acquire? Assume that any other unbalanced forces during the collision are negligible.

0.281 m/s

In the figure, point P is at rest when it is on the x -axis. The linear speed of point P when it reaches the y-axis is closest to

0.35 m/s

The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area should be written as

0.682 m^2

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 uniform disk has a mass of 2.9 kg and a radius of 0.67 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 40 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system?

2.7 kg*m^2/2

A very thin horizontal, 2.00-m long, 5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200-N force pushes downward. At the west end of the beam, a 200-N force pushes upward. What is the angular acceleration of the beam?

240 rad/s^2 north

A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center. A uniform solid cylinder of mass M, radius R, and length 2R rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?

2w/sqrt(5)

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/s^2

A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is 4.07 rad/s at the bottom, what is the height of the inclined plane?

3.25 m

A 1.2-kg spring-activated toy bomb slides on a smooth surface along the xx-axis with a speed of 0.50 m/s. At the origin 0, the bomb explodes into two fragments. Fragment 1 has a mass of 0.40 kg and a speed of 0.90 m/s along the negative y-axis. In the figure, the angle θθ, made by the velocity vector of fragment 2 and the xx-axis, is closest to

31 degrees

What is the result of 1.45 ÷ 3.413 written with the correct number of significant figures?

4.25 x 10^-1

A light triangular plate OAB is in a horizontal plane. Three forces, F1 = 2.0 N, F2 = 7.0 N, and F3 = 8.0 N, act on the plate, which is pivoted about a vertical axes through point O. In the figure, F2 is perpendicular to OB. Consider the counterclockwise sense as positive. The sum of the torques about the vertical axis through point O, acting on the plate due to forces F1, F2, and F3, is closest to

4.6 N*m

The angular acceleration of a wheel is given in rad/s2 by 46 t 3 - 11t 4, where t is in seconds. If the wheel starts from rest at t = 0.00 s, when is the next time the wheel is at rest?

5.2 s

At any angular speed, a certain uniform solid sphere of diameter D has half as much rotational kinetic energy as a certain uniform thin-walled hollow sphere of the same diameter when both are spinning about an axis through their centers. If the mass of the solid sphere is M, the mass of the hollow sphere is

6/5M

Which of the following is an accurate statement? A. The magnitude of a vector is independent of the coordinate system used. B. It is possible to add a scalar quantity to a vector. C.Rotating a vector about an axis passing through the tip of the vector does not change the vector. D. The magnitude of a vector can be zero even though one of its components is not zero. E.Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.

A. The magnitude of a vector is independent of the coordinate system used.

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Compare the time it takes each of them to reach the lake below.

Alice and Tom will reach the surface of the lake at the same time. Submit

You walk 51 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

Answer: 62° N of E How to solve: -find the displacement in the Y direction y=51m+45(cos(60))=73.5 -find the displacement in the X direction x=45(sin(60))=38.97 -find the displacement vector r=38.97i+73.5j -find the angle theta=arctan(y/x)

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.

If two vectors are perpendicular to each other, their cross product must be zero.

False

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that

I2>I1

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.

A ball is thrown directly upward and experiences no air resistance. Which one of the following statements about its motion is correct?

The acceleration is downward during the entire time the ball is in the air.

The graph in the figure shows the force on an object as a function of the elongation caused by that force. Which statement about this object is true?

The object obeys Hooke's law at all points from A to B.

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.

A factory robot drops a 10 kg computer onto a conveyor belt running at 9.7 m/s. The materials are such that μ s = 0.50 and μ k = 0.30 between the belt and the computer. How far is the computer dragged before it is riding smoothly on the belt?

answer: how to solve: a= μ k * g -use v^2-u^2=2*a*d to solve for d

If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance, it will

accelerate but will not spin.

A car needs to generate 75.0 hp in order to maintain a constant velocity of 25.8 m/s on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.)? (1 hp = 746 W)

answer 2.17 x 10^3 How to solve: power= 746 * horsepower -resistive force = power/velocity

Vector A→ = -1.00i+ -2.00j and vector B→ = 3.00 i + 4.00 j. What are the magnitude and direction of vector C→ = 3.00A→ + 2.00B→?

answer 3.61 in a direction 33.7° counterclockwise from the positive x-axis How to solve: -multiply constant into A and B 3(-i-2j)+2(3i+4j) -add i and j vectors =3i+2j -Find magnitude of he vector using sqrt(9+4) = 3.61 -find theta using arctan(y/x)

A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s2 directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall?

answer 66 m/s at -17 degrees how to solve: -Find vertical component v=u+gt u=70sin25 g=-9.8 t=5 -Plug in v=-19.416 -find horizontal component =70cos25=63.44 -find magnitude of components for velocity -find theta using theta=arctan(y/x)

A hobby rocket reaches a height of 62.7 m and lands 200 m from the launch point with no air resistance. What was the angle of launch?

answer: How to solve: theta= arctan(4H/R) H=62.7m R=111m

A box is sliding down an incline tilted at a 11.5° angle above horizontal. The box is initially sliding down the incline at a speed of 1.80 m/s. The coefficient of kinetic friction between the box and the incline is 0.390. How far does the box slide down the incline before coming to rest?

answer: How to solve: -use kinematic equation to find s -F=ma - a=g(sin(theta)-ucos(theta))

An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west. How much work is done on the plane by the air?

answer: -2.71 x 10^8

A satellite orbits the earth a distance of 1.50 × 107 m above the planet's surface and takes 8.65 hours for each revolution about the earth. The earth's radius is 6.38 × 106 m. The acceleration of this satellite is closest to

answer: 0.870 m/s^2 How to solve: -add radius of earth and orbit to get total radius - equation a=v^2/r v= 2piR (circumference)/time -convert time to seconds

How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?

answer: 1.10 MJ How to solve: E=.5m(v^2-u^2)

Bumpers on cars are not of much use in a collision. To see why, calculate the average force a bumper would have to exert if it brought a 1200-kg car (a so-called compact model) to a rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph). (Bumpers are built with springs that compress to provide a stopping force without, hopefully, denting the metal.)

answer: 1.6 x 10^4 How to solve: use v^2=u^2+2as -plug in to find a F = ma -plug in to find force

To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? (You can ignore air resistance.)

answer: 10m How to solve:

An 8.0-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface (see the figure). The bullet remains lodged in the block. The block moves into an ideal massless spring and compresses it by 8.7 cm. The spring constant of the spring is 2400 N/m. The initial velocity of the bullet is closest to

answer: 1100 m/s

A 480-kg car moving at 14.4 m/s hits from behind a 570-kg car moving at 13.3 m/s in the same direction. If the new speed of the heavier car is 14.0 m/s, what is the speed of the lighter car after the collision, assuming that any unbalanced forces on the system are negligibly small?

answer: 13.6 m/s

A car accelerates from 5 m/s to 29.0 m/s} at a rate of 3.00 m/s2. How far does the car travel while accelerating?

answer: 136 how to solve: v^2= u^2+2as -rearrange s=(v^s-u^2)/2a -plug in = (29^2-5^2)/2(3)

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.70 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

answer: 1473 J How to solve: w=Fxd F= coefficient or friction*mg

An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 7.4 cm below the starting point. If instead of having been lowered slowly the object was dropped from rest, how far then would it then stretch the spring at maximum elongation?

answer: 15cm How to solve: Potential energy=mgh

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

answer: 18.5 m/s how to solve: -centripetal force F=(mv^2)/r -frictional force F=coefficient of friction *Normal force(N) N= mg -Set them equal to each other centripetal force=normal force to find v

A 1000 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s. How far does it travel while slowing down?

answer: 18.5m How to solve: -use F=ma to solve for a -use v^2-u^2=2as to solve for s

A potential energy function is given by U(x)=(3.00N)x−(1.00N/m2)x3. At what position or positions is the force equal to zero?

answer: 1m and -1m

An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 6.8 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?

answer: 2.3 m/s How to solve: V= 6.8 x sin(20)

A firecracker breaks up into several pieces, one of which has a mass of 200 g and flies off along the x-axis with a speed of 82.0 m/s. A second piece has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What are the magnitude and direction of the total momentum of these two pieces?

answer: 21.2 kg*m/s at 39.5 from the x-axis

A series of weights connected by very light cords are given an upward acceleration of 4.00 m/s2 by a pull P, as shown in the figure. A, B, and C are the tensions in the connecting cords. The SMALLEST of the three tensions, A, B, and C, is closest to A=20kg B=15kg C=10kg D=5kg

answer: 276N How to solve: A-mg=ma A=m(g+a) =20*(9.8+4)

The figure shows two wires that are tied to a .590 kg mass that revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in the upper wire?

answer: 28N

The scalar product of vector A→ = 3.00 i + 2.00 j and vector B→ is 13.0. Which of the following vectors could be vector B→?

answer: 3.0i + 2.0j how to solve: test answer choices

A roadway for stunt drivers is designed for racecars moving at a speed of 22 m/s. A curved section of the roadway is a circular arc of 820 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?

answer: 3.4 degrees How to solve: =arctan(v^2/Rg)

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x)=(−2.00J⋅m)/x+(4.00J⋅m)/x2. Suppose the particle is moving with a speed of 3.00 m/s when it is located at x=1.00. What is the speed of the object when it is located at x=5.00 m?

answer: 3.67 How to solve: Change in potential energy= change in kinetic energy so set equal

The components of vector A→ are Ax = + 3.90 and Ay = -4.00. What is the angle measured counterclockwise from the +x-axis to vector A→?

answer: 314 degrees How to solve: -theta= arctan(|Ay|/|Ax|) -then think about what quadrant it is for angle from correct axis.

An object attached to an ideal massless spring is pulled across a frictionless surface. If the spring constant is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at 1.2 m/s2, what is the mass of the object?

answer: 33kg How to solve: F=kx ma=kx m=spring constant*stretch/acceleration

A block is on a frictionless horizontal table, on earth. This block accelerates at 3.3 m/s2 when a 70 N horizontal force is applied to it. The block and table are then set up on the moon where the acceleration due to gravity is 1.62 m/s2. What is the weight of the block on the moon?

answer: 34 N How to solve: - Use F=ma to find m -use W=mg to find weight

A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on an object that moves from x = 2.0 m to x = 8.0 m. (Assume an accuracy of 2 significant figures for the numbers on the graph.)

answer: 35J How to solve: work is the area under the curve

In the figure, a T-bar ski tow pulls a skier up a hill inclined at 10° above horizontal. The skier starts from rest and is pulled by a cable that exerts a tension T at an angle of 30° above the surface of the hill. The mass of the skier is 60 kg and the effective coefficient of kinetic friction between the skis and the snow is 0.100. What is the maximum tension in the cable if the starting acceleration is not to exceed 0.400 g?

answer: 431 how to solve: use tension equation

A 150-N box is being pulled horizontally in a wagon accelerating uniformly at 3.00 m/s2. The box does not move relative to the wagon, the coefficient of static friction between the box and the wagon's surface is 0.600, and the coefficient of kinetic friction is 0.400. The friction force on this box is closest to

answer: 45.9 N How to solve: -use W=mg to find m -use F=ma to find F

A 1.20-kg ball is hanging from the end of a rope. The rope hangs at an angle 25.0° from the vertical when a 15.0 m/s horizontal wind is blowing. If the wind's force on the rope is negligible, what drag force does the wind exert on the ball?

answer: 5.48 N How to solve: F=mgtan(theta)

Determine the scalar product of A→ = 7.0 i+ 3.0 j - 2.0 k and B→ = 7.0 i - 1.0 j - 3.0 k.

answer: 52 How to solve: -multiply each vector component by its like component = 49 - 3 + 6 -add/subtract normally =52

Three objects are connected by massless wires over a massless frictionless pulley as shown in the figure. The tension in the wire connecting the 10.0-kg and 15.0-kg objects is measured to be 133 N. What is the mass MMM?

answer: 52.8 kg how to solve:

An object has a position given by r = [2.0 m + (5.00 m/s)t] i + [3.0m−(3.00 m/s^2)t^2] j, where all quantities are in SI units. What is the magnitude of the acceleration of the object at time t = 2.00 s?

answer: 6 m/s^2 How to solve: -take derivative to find velocity -take derivative again to find acceleration

In the figure, a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0. The ball is held at point A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle with no friction and arrives at BBB, with the rope barely under tension. The initial velocity of the ball, at point A, is closest to (circle question)

answer: 6.9

The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes it 0.90 s to reach the floor. What is the mass m of the other block? The pulley has no appreciable mass or friction

answer: 60kg how to solve: -use to solve for a s=ut+1/2at^2 -use T-Mg=Ma to solve for little m T=(mg+ma)

An 8.0-kg block is released from rest, with v1v1v_{1} =0.00 m/s, on a rough incline, as shown in the figure. The block moves a distance of 1.6-m down the incline, in a time interval of 0.80 s, and acquires a velocity of v2= = 4.0 m/s. How much work does gravity do on the block during this process?

answer: 81 How to solve: mg*dcos(90-40)

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

answer: 9.33 m/s^2 how to solve: s=ut+.5at^2 since it starts from rest s=.5at^2 -plug into equation, since there is a change in time you must do two equations 14=.5a(2)^2-.5a(1)^2 14=2a-.5a 28=4a-a 28= 3a 28/3=a

Two objects having masses m1 and m2 are connected to each other as shown in the figure and are released from rest. There is no friction on the table surface or in the pulley. The masses of the pulley and the string connecting the objects are completely negligible. What must be true about the tension T in the string just after the objects are released?

answer: T<(m2)g

The figure shows the graph of the position xxx as a function of time for an object moving in the straight line (the xxx-axis). Which of the following graphs best describes the velocity along the x-axis as a function of time for this object? (looks like an exponential curve starting in the negative y axis)

answer: opposite exponential looking one Why: we can see.. - velocity was initially positive -it decreases with time -it finally become zero

The work performed as a function of time for a process is given by W = at^3 , where a = 2.4 J/s^3. What is the instantaneous power output at t = 1.4 s?

answer:14 W How to solve: power=dW/dt power=3at^2

A rope pulls on the lower block in the figure with a tension force of 20 N. The coefficient of kinetic friction between the lower block and the surface is 0.16. The coefficient of kinetic friction between the lower block and the upper block is also 0.16. The pulley has no appreciable mass or friction. What is the acceleration of the 2.0 kg block?

answer:4.1 m/s^2 how to solve:

A ball rolls across a floor with an acceleration of 0.100 m/s2 in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?

answer:4.15 m/s How to solve: v^2=u^2+2as -plug in (acceleration is negative because it is opposite of velocity) 16=u^2+2*-.1*6 16+1.7=u^2

An 1100-kg car traveling at 27.0 m/s starts to slow down and comes to a complete stop in 578 m. What is the magnitude of the average braking force acting on the car?

answer=690 N How to solve: use F=ma and v^2-u^2=2as

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle. Which arrow best represents the direction of the acceleration of the object at point P? (P is the point on northeast end of the circle)

arrow pointing south west

In a perfectly ELASTIC collision between two perfectly rigid objects

both the momentum and the kinetic energy of the system are conserved. Submit

A dog is standing in the bed of a pickup truck. The bed is coated with ice, causing the force of friction between the dog and the truck to be zero. The truck is initially at rest, and then accelerates to the right, moving along a flat road. As seen from a stationary observer (watching the truck move to the right), the dog

does not move left or right, but the back of the truck moves towards the dog.

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

A car is being towed at constant velocity on a horizontal road using a horizontal chain. The tension in the chain must be equal to the weight of the car in order to maintain constant velocity.

false

On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is

g/2

If an operatic aria lasts for 5.75 min, its length expressed in seconds is x s, where x is

greater than 5.75.

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 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s. If the collision is perfectly elastic, what is the change in the kinetic energy of the 620-g object?

it loses 0.23 J

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 brick is resting on a rough incline as shown in the figure. The friction force acting on the brick, along the incline, is

less than the weight of the brick. Submit

A ball drops some distance and gains 30 J of kinetic energy. Do NOT ignore air resistance. How much gravitational potential energy did the ball lose?

more than 30 J

In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after are given, and no other unbalanced forces act on these blocks. The collision is

not possible because momentum is not conserved.

Two unequal masses M and m (M > m) are connected by a light cord passing over a pulley of negligible mass, as shown in the figure. When released, the system accelerates. Friction is negligible. Which figure below gives the correct free-body force diagrams for the two masses in the moving system?

picture with equal upward force

The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

point x

Suppose the force of the air drag on an object is proportional to the speed of the object and in the direction opposite the object's velocity. If you throw an object upward, the magnitude of its acceleration is greatest

right after the object is released.

which graph represents hookes law?

straight line in the positive x, negative y direction

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass 2m

the lighter box will go twice as high up the incline as the heavier box.

The angular momentum of a system remains constant

when no torque acts on the system.

Two compressible solids are formed into spheres of the same size. The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one. You now increase the pressure on both spheres by the same amount. As a result of the increased pressure, how is the change in volume of sphere two (ΔV2) related to the change in volume of sphere one (ΔV1)?

ΔV2 = 1/2ΔV1