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Classical Mechanics
In the car that decelerates from 30 \text{ kph}30 kph to rest over 15 \text{ cm}15 cm are two 70 \text{ kg}70 kg passengers. One wears a seatbelt and decelerates over 30 \text{ cm}30 cm (with respect to the ground) (two significant figures). The other is not wearing a seatbelt and decelerates over 5 \text{ cm}5 cm* (with respect to the ground). What are the magnitudes of the average external forces acting on the two passengers during their decelerations? (Careful with significant figures: do both answers have the same precision?)
a) With a seatbelt? _____ \text{kN}kN.
b) Without a seatbelt? _____ \text{kN}kN.
Please separate your answers with a comma. Example: a, b
a) With a seatbelt? _____ \text{kN}kN.
b) Without a seatbelt? _____ \text{kN}kN.
Please separate your answers with a comma. Example: a, b
Classical Mechanics
In Doppler's effect the observed frequency of waves in case when observer is in motion, depends upon the relative relative velocity between source and observer. But from Michealson Morley experiment speed of light is independent of relative motion between source and observer.Why is it so?
Classical Mechanics
A ball of mass 100g is thrown vertically upwards from a point 2m above ground level with a speed of 14m/s.
a. With an origin at ground level, find the total mechanical energy of the ball when it is travelling at speed v m/s at a heigh h m.
b. Assuming that mechanical energy is conserved show that v^2+20h=236
c. Calculate the greatest height reached by the ball
d. Calculate the speed with which the ball hits the ground
a. With an origin at ground level, find the total mechanical energy of the ball when it is travelling at speed v m/s at a heigh h m.
b. Assuming that mechanical energy is conserved show that v^2+20h=236
c. Calculate the greatest height reached by the ball
d. Calculate the speed with which the ball hits the ground
Classical Mechanics
A cable car of mass 1200 kg moves 2km up a slope inclined at 30 degrees to the horizontal at a constant speed. If the resistance to motion is 400N find the work done by the tension in the cable.
Classical Mechanics
In the car that decelerates from 30 kph to rest over 15 cm are two 70 kg passengers. One wears a seatbelt and decelerates over 30 cm (with respect to the ground) (two significant figures). The other is not wearing a seatbelt and decelerates over 5 cm* (with respect to the ground). What are the magnitudes of the average external forces acting on the two passengers during their decelerations? (Careful with significant figures: do both answers have the same precision?)
a) With a seatbelt? _____ kN.
b) Without a seatbelt? _____ kN.
Please separate your answers with a comma. Example: a, b
This deceleration occurs when he strikes a part of the car, which is by then stationary. The 5 cm is the passenger's own crumple zone, and this is where the injuries occur.
a) With a seatbelt? _____ kN.
b) Without a seatbelt? _____ kN.
Please separate your answers with a comma. Example: a, b
This deceleration occurs when he strikes a part of the car, which is by then stationary. The 5 cm is the passenger's own crumple zone, and this is where the injuries occur.
Classical Mechanics
In most calculations, we use W \approx mgW≈mg. But we know that, for large changes in altitude, we need to use W∝1/r2. How far above the Earth's surface can we use W = mgW=mg before our systematic error reaches 1%? Use only the information given in this question, and the radius of the Earth re=6400 km. Do not explicitly use GG or the mass of the Earth, and do the calculation for the pole so that we don't worry about the effect of centripetal acceleration.
Hint: Does gg become larger or smaller with altitude?
Altitude= ___ \text{km}km (to one significant figure)
Hint: Does gg become larger or smaller with altitude?
Altitude= ___ \text{km}km (to one significant figure)
Classical Mechanics
Consider the mechanical energy of a body in geostationary orbit above the Earth's equator, at rGS =42000 km.
Consider the mechanical energy of the same body on Earth at the South pole, at re =6400 km. For this problem, we consider the Earth to be spherical. (Remember, the object at the equator is in orbit, the object at the Pole is not in orbit.)
G=6.67×10^−11 Nm^2 kg^−2, and the mass of the Earth is M=5.97×10^24 kg
What is the difference in the mechanical energy per kilogram between the two?
E =E= ___ MJ.kg^−1 (to two significant figures, don't use scientific notation)
How much more mechanical energy per kilogram does an object on the ground at the Equator than on the ground at the Pole?
E =E= ___ MJ.kg^−1
(2 sig figs, do not use scientific notation)
Consider the mechanical energy of the same body on Earth at the South pole, at re =6400 km. For this problem, we consider the Earth to be spherical. (Remember, the object at the equator is in orbit, the object at the Pole is not in orbit.)
G=6.67×10^−11 Nm^2 kg^−2, and the mass of the Earth is M=5.97×10^24 kg
What is the difference in the mechanical energy per kilogram between the two?
E =E= ___ MJ.kg^−1 (to two significant figures, don't use scientific notation)
How much more mechanical energy per kilogram does an object on the ground at the Equator than on the ground at the Pole?
E =E= ___ MJ.kg^−1
(2 sig figs, do not use scientific notation)
Classical Mechanics
9. A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18 kgm2. She then tucks into a small ball, decreasing this moment of inertia to 3.6 kgm2. While tucked, she makes two complete revolutions in 1 sec. If she had not tucked at all, how many revolutions would she have made in the 1.5 sec from board to water?
10. A skater has a moment of inertia of 3 kgm2 when her arms are stretched out and 1kgm2 when her arms are brought to her sides. She starts to spin at the rate of 1 rev/sec when her arms are outstretched, and then pulls her arms to her sides. a. What is the final angular velocity? b. How much work did she have to do?
10. A skater has a moment of inertia of 3 kgm2 when her arms are stretched out and 1kgm2 when her arms are brought to her sides. She starts to spin at the rate of 1 rev/sec when her arms are outstretched, and then pulls her arms to her sides. a. What is the final angular velocity? b. How much work did she have to do?
Classical Mechanics
7. A mass (M1 = 5 kg) is connected by a light cord to a mass (M2 = 4 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius=0.20 m) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s2. What is the moment of inertia of the pulley?
8. A playground merry-go-round has a disk-shaped platform that rotates with negligible friction about a vertical axis. The disk has a mass of 200 Kg and a radius of 2 m. A 40-Kg child rides at the center of the merry-go-round while a playmate sets it turning at 0.35 rev/sec. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning? (HINT: Treat the child as a particle)
8. A playground merry-go-round has a disk-shaped platform that rotates with negligible friction about a vertical axis. The disk has a mass of 200 Kg and a radius of 2 m. A 40-Kg child rides at the center of the merry-go-round while a playmate sets it turning at 0.35 rev/sec. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning? (HINT: Treat the child as a particle)
Classical Mechanics
5. A 15-kg object and a 10-kg object are suspended, joined by a cord that passes over a pulley with a radius of 15 cm and a mass of 3 kg. The cord has a negligible mass and does not slip on the pulley. Treat the pulley as a uniform disk, and determine the linear acceleration of the two objects after the objects are released from rest.
6. A block of mass m1 = 2 kg and a block of mass m2 = 6 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10 kg. These blocks are allowed to move on a fixed block-wedge of angle = 30 degrees. Draw free-body diagrams of both blocks and of the pulley. Determine (a) the acceleration of the two blocks, and (b) the tensions in the string on both sides of the pulley.
6. A block of mass m1 = 2 kg and a block of mass m2 = 6 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10 kg. These blocks are allowed to move on a fixed block-wedge of angle = 30 degrees. Draw free-body diagrams of both blocks and of the pulley. Determine (a) the acceleration of the two blocks, and (b) the tensions in the string on both sides of the pulley.
