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Classical Mechanics
1. At the radius of the earth's orbit, the intensity of sunlight is I = 1.4 kW.m^-2 . (This means that 1.4 kW.m^-2 passes through 1 square metre at right angles to the sun's rays.) The solar array in the previous question consists of 10 panels, each with area A = 1.6 m^2 . Under optimal conditions - with the sun at right angles to the array and no clouds in the sky - the array produces P out = 2.3 kW .
What is the efficiency of the array? Power out/power in = _____ %.
2. Here is an extract from our electricity bill. The colored text has been added to highlight the rate, with the 'rate' being the price per kW.hr:
We buy energy at:
Used energy x rate = cost
92 days ( 294.3 kWh) 24.9000 c 73.27 dollars
Energy Purchased x rate = credit
92 days ( 883.4 kWh) 6.6000 c 58.30 dollars
What is the efficiency of the array? Power out/power in = _____ %.
2. Here is an extract from our electricity bill. The colored text has been added to highlight the rate, with the 'rate' being the price per kW.hr:
We buy energy at:
Used energy x rate = cost
92 days ( 294.3 kWh) 24.9000 c 73.27 dollars
Energy Purchased x rate = credit
92 days ( 883.4 kWh) 6.6000 c 58.30 dollars
Classical Mechanics
1. A car has a drag coefficient Cd = 0.30, a frontal area of A = 1.9 m^2 and a mass 1.2 tonnes. It has a coefficient of rolling resistance, Cr = 0.012. The rolling resistance is a force Fr = CrN, where N is the normal force. Hint: Retain accurate values until the final calculation, but remember significant figures.
i) What is Fr when traveling at v = 110 kph on a horizontal road?
ii) What power (in kilowatts) is required to overcome Fr at this speed?
2. A car has a drag coefficient Cd = 0.30, a frontal area of A = 1.9^2 m, a mass 1.2 tonnes and a coefficient of rolling resistance, Cr, = 0.012. It is traveling up a hill with a slope of 1 in 20 at 110 kph. At what rate is it doing work against gravity (i.e. at what rate is it increasing its gravitational potential energy)?
Pg= _____ kW.
A 1:20 grade means that it rises 1 m for every 20 m traveled along the road: sin(θ)=1/20.
i) What is Fr when traveling at v = 110 kph on a horizontal road?
ii) What power (in kilowatts) is required to overcome Fr at this speed?
2. A car has a drag coefficient Cd = 0.30, a frontal area of A = 1.9^2 m, a mass 1.2 tonnes and a coefficient of rolling resistance, Cr, = 0.012. It is traveling up a hill with a slope of 1 in 20 at 110 kph. At what rate is it doing work against gravity (i.e. at what rate is it increasing its gravitational potential energy)?
Pg= _____ kW.
A 1:20 grade means that it rises 1 m for every 20 m traveled along the road: sin(θ)=1/20.
Classical Mechanics
1. I drag a mass m = 21 kg in a straight line, along a horizontal surface, a distance D = 23 m . I drag it at constant speed v = 0.90 m.s^-1 in a straight line using a horizontal force. The coefficients of friction are μs = 1.2 and μk = 1.1. How much work do I do?
2. A rubber band has mass m = 0.30 g and a spring constant k =15 N.m^-1 . I stretch it by 5.0 cm (which in this case doubles its length). Assume the rubber band behaves as a Hooke's law spring. Assume that, when you launch the rubber band, all of the stored potential energy is converted into kinetic energy. How fast is it at the launch?
3. A car has a drag coefficient Cd = 0.30, a frontal area of A = 1.9 m^2 and a mass 1.2 tonnes. The density of air is 1.2 kg.m^-3. Hint: Retain accurate values until the final calculation, but remember significant figures.
i) What is the drag force when it is traveling at v = 110 kph in a straight line?
ii) What power (in kilowatts) is required to overcome the drag force at this speed?
2. A rubber band has mass m = 0.30 g and a spring constant k =15 N.m^-1 . I stretch it by 5.0 cm (which in this case doubles its length). Assume the rubber band behaves as a Hooke's law spring. Assume that, when you launch the rubber band, all of the stored potential energy is converted into kinetic energy. How fast is it at the launch?
3. A car has a drag coefficient Cd = 0.30, a frontal area of A = 1.9 m^2 and a mass 1.2 tonnes. The density of air is 1.2 kg.m^-3. Hint: Retain accurate values until the final calculation, but remember significant figures.
i) What is the drag force when it is traveling at v = 110 kph in a straight line?
ii) What power (in kilowatts) is required to overcome the drag force at this speed?
Classical Mechanics
1. A corner in a flat road has a constant radius of r = 25 m. Air resistance and rolling resistance are zero. And the car is traveling at constant speed. What is the maximum speed our car can go round this corner without skidding? For a reasonably clean, dry road, take the coefficients of static and kinetic friction to be μs = 1.0 and μk=0.80. Hint: What horizontal force is acting on the car? Maximum speed _____ kph
2. You place a mass m = 25 on a book and slowly increase the angle θ that the book makes with the horizontal. At a critical angle θc = 43∘, the mass starts to slide so you hold the angle constant. The mass takes 0.75 s to slide a distance of 17 cm to the edge of the book. Assume that the values of μs are uniform all over the book. What is the value of μs ?
3. Using the information from #2 : What is the value of μk ?
2. You place a mass m = 25 on a book and slowly increase the angle θ that the book makes with the horizontal. At a critical angle θc = 43∘, the mass starts to slide so you hold the angle constant. The mass takes 0.75 s to slide a distance of 17 cm to the edge of the book. Assume that the values of μs are uniform all over the book. What is the value of μs ?
3. Using the information from #2 : What is the value of μk ?
Classical Mechanics
1. Your doctor has told you to watch your weight. Of course, your weight comprises two factors, so you assume that she wants you to watch both your mass and the local value of g. Which explains why you are carrying a small mass m on an elastic band wherever you go. Most of the time, the elastic band is stretched by a distance of 2.1 cm. However, when you have finished lunch, you go into a very tall building and take the high speed lift. Soon after the doors close, you notice that the band is stretched by a total distance of 3.5 cm.
a) At what rate is the lift accelerating?
b) Your doctor will want to know the factor by which your weight has increased after that lunch. Suppose that you stand on scales in the lift while it is accelerating as described above. According to the scales, your weight has increased by a factor of _____ .
a) At what rate is the lift accelerating?
b) Your doctor will want to know the factor by which your weight has increased after that lunch. Suppose that you stand on scales in the lift while it is accelerating as described above. According to the scales, your weight has increased by a factor of _____ .
Classical Mechanics
1. Jim's mass is m = 62 kg. He is standing in a lift, with no motion relative to the lift.
a) The lift accelerates upwards at 2.0 m.s^-2. What is the magnitude of the force the floor of the lift exerts on Jim?
b) Later, the lift accelerates downwards at 2.0 m.s^-2. What is the magnitude of the force the floor of the lift exerts on Jim?
c) Just suppose that the lift were to accelerate downwards at 10.0 m.s^-2. What force would the floor of the lift exert on Jim?
a) The lift accelerates upwards at 2.0 m.s^-2. What is the magnitude of the force the floor of the lift exerts on Jim?
b) Later, the lift accelerates downwards at 2.0 m.s^-2. What is the magnitude of the force the floor of the lift exerts on Jim?
c) Just suppose that the lift were to accelerate downwards at 10.0 m.s^-2. What force would the floor of the lift exert on Jim?
Classical Mechanics
1. On the moon, an eagle feather dropped by Apollo astronauts falls with an acceleration of 1.6 m.s^-2. Ted, the astronaut who has done this experiment, has a mass of 79 kg on Earth. Using these values answer the following questions:
a) What is Ted's weight (on Earth)?
b) What is his weight on the moon?
c) What is his mass on the moon?
2. My bathroom scales read in kilograms, meaning that, if I put a mass m on top of them, in mechanical equilibrium, the dial (accurately) shows the mass m in kg. The scales are light.
I apply a force of 85 newtons to the scales. What do they read?
a) What is Ted's weight (on Earth)?
b) What is his weight on the moon?
c) What is his mass on the moon?
2. My bathroom scales read in kilograms, meaning that, if I put a mass m on top of them, in mechanical equilibrium, the dial (accurately) shows the mass m in kg. The scales are light.
I apply a force of 85 newtons to the scales. What do they read?
Classical Mechanics
1.What is the average force between a cricket bat and ball during collision? Let's assume that the ball's initial and final velocities with respect to the bat are anti parallel and have magnitudes of about 100 kph. Suppose the collision lasts about 1 ms. A cricket ball has a mass of 0.16 kg. What is average force between bat and ball ?
Bowlers bowl at over 150 kph and, even though air resistance slows the ball down considerably by the time it reaches the batsman, the bat is often traveling rapidly in the other direction. So both velocities used here are probably exceeded substantially in professional games. I'm guessing that, because the cricket ball is hard, the collision might last less about 1 ms.
2. Parachutist and parachute have a combined mass of 93 kg. They are traveling vertically downwards at a constant speed of 0.30 m.s^-1. What is the magnitude of the force of air resistance on them ( in newtons and correct sig fig).
Bowlers bowl at over 150 kph and, even though air resistance slows the ball down considerably by the time it reaches the batsman, the bat is often traveling rapidly in the other direction. So both velocities used here are probably exceeded substantially in professional games. I'm guessing that, because the cricket ball is hard, the collision might last less about 1 ms.
2. Parachutist and parachute have a combined mass of 93 kg. They are traveling vertically downwards at a constant speed of 0.30 m.s^-1. What is the magnitude of the force of air resistance on them ( in newtons and correct sig fig).
Classical Mechanics
1. The Earth is 8 light minutes from the sun and the speed of light is 3 × 10^8 m/s. Let's assume that earth's orbit is exactly circular. Its mass is 5.972 × 10^24 kg.
Using the values given above (and your knowledge about time units), determine the magnitude of the gravitational force that the Sun exerts on the Earth.
The magnitude of the force is _____ newtons.
2. How does the force that the Sun exerts on the Earth compare with the Earth's force on the sun?
A. The magnitude of the force the earth exerts on the sun equals that of the force that the sun exerts on the earth.
B. The magnitude of the force the earth exerts on the sun exceeds that of the force that the sun exerts on the earth.
C. The magnitude of the force the earth exerts on the sun is less than that of the force that the sun exerts on the earth.
Using the values given above (and your knowledge about time units), determine the magnitude of the gravitational force that the Sun exerts on the Earth.
The magnitude of the force is _____ newtons.
2. How does the force that the Sun exerts on the Earth compare with the Earth's force on the sun?
A. The magnitude of the force the earth exerts on the sun equals that of the force that the sun exerts on the earth.
B. The magnitude of the force the earth exerts on the sun exceeds that of the force that the sun exerts on the earth.
C. The magnitude of the force the earth exerts on the sun is less than that of the force that the sun exerts on the earth.
Classical Mechanics
1. Airplanes usually use their wings to turn: When the plane is tilted at an angle θ, the lift (L) from the wings provides a vertical component and a horizontal component. The direction of the lift is in the plane of symmetry of the plane (up from the wings). Suppose that the plane is tilted at an angle θ = 29.0∘ and that it is making an exactly horizontal, circular path at a uniform speed of 455 kph. Take g = 9.80 m.s^-2 for three significant figures (the value at Sydney).
What is the radius of its turn? _____ km.
2. During this turn of the airplane, suppose that a passenger puts a nearly full glass of water on the tray table in front of her. What happens to the water? The plane is turning right for the passenger.
a) It spills out of the glass to the left
b) It spills out of the glass to the right
c) It stays in the glass, with its surface parallel to the tray table.
d) None of these.
What is the radius of its turn? _____ km.
2. During this turn of the airplane, suppose that a passenger puts a nearly full glass of water on the tray table in front of her. What happens to the water? The plane is turning right for the passenger.
a) It spills out of the glass to the left
b) It spills out of the glass to the right
c) It stays in the glass, with its surface parallel to the tray table.
d) None of these.
