PHYSICS 201 TEST 2

What is the change in gravitational potential energy of a 9.00- kg mass that is carried from the surface of the earth to a distance of one earth radius above the surface?

(.5)(mgr) r=radius of the earth=6.371e6

You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 47.4 N·m. Using the data in the drawing below (L = 0.294 m and θ = 49.8°), determine the magnitude F of the force that you must exert on the wrench.

Torque=LFsin(theta)

A solid disk rotates in the horizontal plane at an angular velocity of 0.0692 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.126 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.420 m from the axis. The sand in the ring has a mass of 0.489 kg. After all the sand is in place, what is the angular velocity of the disk?

Vangualarvelocity=(Velocityofdisk)(Inertiaofdisk)/(inertiadisk+inertiaofsand) Inertiaofsand=(massofsand)(radius^2)

A mine car, whose mass is m1 = 440 kg, rolls at a speed of v1 = 0.493 m/s on a horizontal track, as the drawing below shows. An m2 = 154 kg chunk of coal has a speed of v2 = 0.781 m/s when it leaves the chute. Assume θ = 22.9°. Determine the velocity of the car/coal system after the coal has come to rest in the car.

m2v2costheta+(m1)(v1)/(m2+m1)

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing below illustrates. The crest of the second hill is circular, with a radius of r = 37.7 m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

r/2

A 326- g stationary air-track glider is attached to the end of an air track by a compressible spring with spring constant k = 7.42 N/m (see the figure). A 163- g glider moving at 1.27 m/s collides elastically with the stationary glider. How far does the spring compress? Assume that the air track is very much heavier than the gliders.

v2=(2m1/m1+m2)vi x=squareroot(m2(v2)^2^)/k

A fireworks rocket is moving at a speed of v = 47.5 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v1 at an angle of theta1 = 29.6° and v2 at an angle of theta2 = 60.4° as shown in the drawing below. What is the magnitude of v1?

v= 2(Vo)/Costheta1+(Sintheta1/Sintheta2)(Costheta2)

How fast must you project an object for it to reach a height equal to the moon's distance from the earth? Ignore the gravitational attraction of the moon.

v=squareroot(2ghRE)/(RE+h) RE=6.38e6 h=3.76e8

A woman who weighs 4.81E+2 N is leaning against a smooth vertical wall, as the drawing below shows. As shown, h1 = 1.36 m, h2 = 0.380 m and θ = 61.9°. Calculate the force FN (directed perpendicular to the wall) exerted on her shoulders by the wall.

w(h1)cos(theta)-Fn(h1+h2)sin(theta)=0

A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. The thrust of its engines is 2.12 x 105 N. In being launched from rest it moves through a distance of 85.3 m and has a kinetic energy of 4.41 x 107 J at lift-off. What is the work done on the jet by the catapult?

(F)(d)+W=KE

A 700- kg car collides with a 1200- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 20.0 km/h in a direction of 40 o with respect to the positive x axis. The heavier car moves at 23 km/h at -48 o with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? What was the initial direction (as measured counterclockwise from the x-axis)?

(a) m2v2cos(theta2) m1v1cos(theta1) 1-2 m2v2sin(theta2) m1v1sin(theta1) 3-4 square root (1-2)^2^+(3-4)^2^=pre-answer/m1=initial speed (b)arctan( y/x)=direction 360-direction

Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 9.66 rad/s. The wheel has a radius of .450 m. If you ride the bike for 39.4 min, how far would you have gone if the bike could move?

(circumference)(# of total revolutions)=answer C=2piR convert min to seconds 1 rad= .16 rev seconds times rev

Consider the situation shown in the figure but with the 4.0- kg mass replaced by a 6.1- kg mass. The frictional coefficient is 0.29. Find the acceleration of the system. What is the tension T1? What is the tension T2?

1) m3(g)-f(m1+m2)g)/m1+m2+m3 2)T=m1(a+(f)(g)) 3)m3(g-a)

A ball of mass 0.40 kg is fired with velocity 160 m/s into the barrel of a spring gun of mass 2.4 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?

KEintial=1/2(m)(Vinital)^2^ KEfinal=1/2(m+M)(Vfinal)^2^ Vfinal=m/(m+M)Vinital KE=KEfinal-KEinital *absolute value* KE/KEinital=initial kinetic energy stored in the spring

The puck in the figure below has a mass of 0.117 kg. Its original distance from the center of rotation is 44.4 cm, and the puck is moving with a speed of 71.0 cm/s. The string is pulled downward 15.5 cm through the hole in the frictionless table. Determine the work done on the puck.

Kef-Kei=KE Kef=.5mVf2 Kei=.5mfVi2 Vf=(Ri/Vi)(RF) RF= Ri-downward pull

The drawing below shows a person whose weight is W = 559 N doing push-ups. Assume L1 = 0.883 m and L2 = 0.426 m. Calculate the normal force exerted by the floor on each hand, assuming that the person holds this position.

L1 x W/ L1+L2 divide answer by 2 for each arm

The escape speed from a distant planet is 48 km/s. If the acceleration of gravity on the planet surface is 15.5 m/s2, what is the radius of the planet?

R= v^2^/2g convert escape speed to meters remember this g is the the gravity on the plant not 9.81

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.09E4 rad/s to an an angular speed of 3.04e4 rad/s. In the process, the bit turns through 1.80E4 rad. assuming a constant angular acceleration, how long would take the bit to reach it maximum speed of 7.71e4 rad/s, starting from rest?

Vf(squared)=Vi(squared)+2(a)(s) v=u+at

A rocket is projected upward from the earth's surface (r = RE) with an initial speed v0 that carries it to a distance r = 1.6 RE from the center of the earth. What is the launch speed v0? Assume that air friction can be ignored.

Vinital=squareroot2[(Gme/Ri)-(Gme/Rf)] G=6.674e-11 me=5.972e24 Re=6.38e6 Ri=Re Rf=distnace given x Re

A 1.13E+2 kg crate is being pushed across a horizontal floor by a force P that makes an angle of 33.5° below the horizontal. The coefficient of kinetic friction is 0.202. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

cos(theta)p-sin(theta)pf=mgf *solve for p*

A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 4.0- cm radius. A dumbbell-shaped "flywheel" made from two 0.500- kg masses is attached to one end of the shaft and perpendicular to its axis (see the figure). The mass is released from rest and allowed to fall 0.8 m to the floor. It reaches a speed of 0.9609 m/s just before striking the floor. How far apart are the masses of the dumbbell?

gh=.5(v)^2^+.5R^2^w^2^ w=v/r multiply the answer by 2