A simple pendulum consists of a small object of mass m= 0.150 kg suspended from a support stand by a light string. The string has a length L= 0.750 m. The string has an initial position given by θ= 65.0° relative to the vertical. The pendulum is released from rest. Air resistance is negligible during the subsequent motion of the pendulum.

a)Calculate the work done by gravity on the pendulum as it moves from its initial position to the lowest point of its semicircular arc. b)Calculate the speed of the object as it moves through the lowest point of its semicircular arc.

c)Calculate the tension in the string right as the object is moving through the lowest point of its semicircular arc.

d)Repeat part b) using the conservation of total mechanical energy. (Is the total mechanical energy of the pendulum conserved?)

The spin cycles of a washing machine have two angular speeds, 416 rev/min and 632 rev/min . The internal diameter of the drum is 0.560 m

Part A

What is the ratio of the maximum radial force on the laundry for the higher angular speed to that for the lower speed? (F higher/F lower)=?

Part B

What is the ratio of the maximum tangential speed of the laundry for the higher angular speed to that for the lower speed? (V higher/ V lower)=?

Part C

Find the laundry's maximum tangential speed . (m/s)

Part D

Find the laundry's maximum radial acceleration, in terms of g . (a rad=? g)

A converging lens has a focal length of 21.1 cm.

(a) Locate the object if a real image is located at a distance from the lens of 63.3 cm.

(b) Locate the object if a real image is located at a distance from the lens of 105.5 cm.

(c) Locate the object if a virtual image is located at a distance from the lens of -63.3 cm.

(d) Locate the object if a virtual image is located at a distance from the lens of -105.5 cm.

A box of mass 10.2 kg with an initial velocity of 2.1 m/s slides down a plane, inclined at 28◦ with respect to the horizontal. The coefficient of kinetic friction is 0.69. The box stops after sliding a distance x.

a. How far does the box slide? The acceleration due to gravity is 9.8 m/s 2 . The positive x-direction is down the plane. Answer in units of m.

b. What is the the work done by friction? Answer in units of J.

c. What is the work done by the normal force? Answer in units of J.

d. What is the magnitude of the work done by gravity? Answer in units of J.

e. What is the magnitude of the instantaneous power generated by friction half way between the initial and final positions? Answer in units of W.

f. What is the magnitude of the average power generated by friction from start to stop? Answer in units of W.

Two satellites, A and B, both of mass m = 115 kg, move in the same circular orbit of radius r = 7.57 106 m around Earth but in opposite senses of rotation and therefore on a collision course.

a) What is the total mechanical energy E_A + E_B of the two satellites + Earth system before the collision?

b)If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), what is the total mechanical energy immediately after the collision?

answer has to be in J

Emily throws a soccer ball out of her dorm window to Allison, who is waiting below to catch it.

If Emily throws the ball at an angle of 30∘ below the horizontal with a speed of 14m/s, how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 8.0m.

Given the mass of two blocks that collide, and the velocities of each block before and after the collision, be able to determine whether the collision was elastic, partially or completely inelastic, or not possible since an unnamed external force would be necessary to change the momentum, and/or kinetic energy of the system.

Please explain in simplest terms and give an example using units given.

A 0.313-m-thick sheet of ice covers a lake. The air temperature at the ice surface is -15.9 °C. In 4.70 minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.313 m. Calculate the number of millimeters by which the ice thickens. Do not enter unit.

explain why it makes some sense that a large temperature difference enables greater efficiency.

A 4100 kg open railroad car coasts along with a constant speed of 9.90 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 5.00 kg/min . Ignoring friction with the tracks, what is the speed of the car after 80.0 min ?

An alpha (?) particle is the nucleus of a 4He atom and consists of 2 neutrons and two protons bound together. Let's take apart an ? particle, step by step, looking at the energy required at each step. To do so, we may want to use the following atomic masses: 4He 4.0026 u 2H 2.0141 u 3H 3.01605 u 2H 1.00783 u p 1.00728 u n 1.00867 u e 5.48

two cylinders with the radius r= 0.650 m are rolled with out slipping down an incline that desends a vertical distance of 2.45 meters each cylinder has equal mass m=3.68kg but one is solid the other is hollow shell

a) what is the center mass velocity of the solid cylinder at the bottom of the incline

b) what is the center mass velocity of the holllow cylinder of the botom of the incline

c) what is the angular frequency of each cylinder when it reaches the bottom of the incline

Neutron Decay 4 On their own, neutrons are unstable particles with a half-life of 618 s when at rest. They decay into a proton, an electron and an electron antineutrino. Half-life is the time that it takes half of a collection of unstable particles to decay.

a- The highest energy neutrons produced in a nuclear reactor are traveling at about %15 of the speed of light, About how many seconds is longer in this half - life for these neutrons?

b . If a bunch of high energy neutrons is emitted from the sun at about 0.88c and travels to earth , some 150 million km away , will more than half or less than half of the neutrons make it to earth before turning into protons ? Show how you reached your conclusion

A doughnut contains about 302 Calories. (Note: These are "food" Calories.) After eating this doughnut, you decide to compensate by taking the stairs instead of using the elevator. If each stair has a height of 22 cm, how many stairs must you climb to compensate for the doughnut? Assume all the energy in the doughnut can be converted to mechanical energy. (Take 75 kg as the mass of a typical person.)

A mass m = 78 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.4 m and finally a flat straight section at the same height as the center of the loop (15.4 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.)

What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track?

What height above the ground must the mass begin to make it around the loop-the-loop?

If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop?

If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (15.4 m off the ground)?

Now a spring with spring constant k = 1.8 × 10⁴ N/m is used on the final flat surface to stop the mass. How far does the spring compress?

It turns out the engineers designing the loop-the-loop didn’t really know physics – when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning.

How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track?

The work done by the normal force on the mass (during the initial fall) is: