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Classical Mechanics
1. Jane's brother Andrew leaves home for school at 8:00 am. He walks at 4.2 kph. At 8:20 am Jane discovers that Andrew has left his homework at home. She decides to follow him on her bicycle and give him his homework, but she wants to be back home in time for an online test at 9:00 am. What is the minimum constant speed at which she needs to ride?
2. A car accelerates with a constant acceleration of 2.1 m/ s^2 along a long straight road. How long does it take the car to accelerate from 100 kph to 110 kph, and how far does it travel while doing so? [ take the speeds as three significant figures.]
3. A (field) hockey player is running north at a speed of 8 m/s . A ball is coming directly towards her from the north at a speed of 18 m/s. She swings her stick forward, directly north, at a speed of 6 m/s measured in her own frame of reference. What is the speed of the ball with respect to the hockey stick?
2. A car accelerates with a constant acceleration of 2.1 m/ s^2 along a long straight road. How long does it take the car to accelerate from 100 kph to 110 kph, and how far does it travel while doing so? [ take the speeds as three significant figures.]
3. A (field) hockey player is running north at a speed of 8 m/s . A ball is coming directly towards her from the north at a speed of 18 m/s. She swings her stick forward, directly north, at a speed of 6 m/s measured in her own frame of reference. What is the speed of the ball with respect to the hockey stick?
Classical Mechanics
In the US, lengths are often measured in inches, feet, yards and miles. Let's do some conversions. The definition of the inch is: 1 inch = 25.4 mm, exactly. A foot is 12 inches and a mile is 5280 ft, exactly. A centimetre is exactly 0.01 m or 10 mm.
Sammy is 5 feet and 5.3 inches tall. Mark all the true statements below. Use the appropriate number of sig figs.):
A. Sammy is 1.66 m tall.
B. Sammy is less than 0.5 m tall.
C. Sammy is between 1600 and 1700 mm tall.
D. Sammy is more than 168 cm tall.
E. Sammy is 55.3 inches tall
F. Sammy is more than 60 inches tall
G. Sammy is 5.44 feet tall.
H. Sammy is 5.4 feet tall.
I. It would take about 90 000 Sammies, lying head to toe to span the entire Victoria's 90 kile beach.
J. It would take about 100 000 Sammies, lying head to toe to span the entire Victoria's 90 kile beach.
Sammy is 5 feet and 5.3 inches tall. Mark all the true statements below. Use the appropriate number of sig figs.):
A. Sammy is 1.66 m tall.
B. Sammy is less than 0.5 m tall.
C. Sammy is between 1600 and 1700 mm tall.
D. Sammy is more than 168 cm tall.
E. Sammy is 55.3 inches tall
F. Sammy is more than 60 inches tall
G. Sammy is 5.44 feet tall.
H. Sammy is 5.4 feet tall.
I. It would take about 90 000 Sammies, lying head to toe to span the entire Victoria's 90 kile beach.
J. It would take about 100 000 Sammies, lying head to toe to span the entire Victoria's 90 kile beach.
Classical Mechanics
1. How many heartbeats in a typical human lifetime? You will provide the data from your general knowledge. Write your answer as a number (NOT as a power of ten).
2. Estimate the mass of water on the earth. The density of water is 1000 kg/ m^3 . Here are some approximations you can use:
Compared with the oceans, lakes and rivers are tiny. Clouds have very low density. There is (still) lots of ice in the polar regions, but much less area than in the oceans. So neglect all except the oceans, which cover roughly 2/3 of the earth.
Looking at charts of the oceans, we see that the depth is typically several thousand m (and a serious search tells me the average depth is 4700 m). The radius of the earth is about 6000 km. The surface area of a sphere is 4πR^2. This is an order or magnitude question. Express your answer in kg, as a power of 10. For example, if you think the answer is 10^4, then write 10^4.
2. Estimate the mass of water on the earth. The density of water is 1000 kg/ m^3 . Here are some approximations you can use:
Compared with the oceans, lakes and rivers are tiny. Clouds have very low density. There is (still) lots of ice in the polar regions, but much less area than in the oceans. So neglect all except the oceans, which cover roughly 2/3 of the earth.
Looking at charts of the oceans, we see that the depth is typically several thousand m (and a serious search tells me the average depth is 4700 m). The radius of the earth is about 6000 km. The surface area of a sphere is 4πR^2. This is an order or magnitude question. Express your answer in kg, as a power of 10. For example, if you think the answer is 10^4, then write 10^4.
Classical Mechanics
1. Subtracting vectors. What is the direction of North minus West?
2. The Vector A in the (x,y) plane has a magnitude A= 3.2 and makes angle Theta = 125 degrees with the x-axis, where theta is measured in the geometric or anticlockwise sense. What are the components of vector A in the x and y directions? Use the correct number of sig figs.
3. How much of you is not vacuum? Outside of the nucleus, an atom contains mostly empty space. Estimate the fraction of the volume of an atom that is occupied by the nucleus. Assume that a typical atom has a linear dimension of about 0.1 nm and that a typical nuclear dimension is about 1 fm. Give your answer as a power of ten.
4. How many revolutions does the drive shaft of a truck engine make during its lifetime? Inputs: Let's suppose that the truck travels a million km (1 billion m) at an average speed of 80 km per hour. The engine turns at a rate of 2000 revolutions per minute.Give your answer as a number (not a power of ten).
2. The Vector A in the (x,y) plane has a magnitude A= 3.2 and makes angle Theta = 125 degrees with the x-axis, where theta is measured in the geometric or anticlockwise sense. What are the components of vector A in the x and y directions? Use the correct number of sig figs.
3. How much of you is not vacuum? Outside of the nucleus, an atom contains mostly empty space. Estimate the fraction of the volume of an atom that is occupied by the nucleus. Assume that a typical atom has a linear dimension of about 0.1 nm and that a typical nuclear dimension is about 1 fm. Give your answer as a power of ten.
4. How many revolutions does the drive shaft of a truck engine make during its lifetime? Inputs: Let's suppose that the truck travels a million km (1 billion m) at an average speed of 80 km per hour. The engine turns at a rate of 2000 revolutions per minute.Give your answer as a number (not a power of ten).
Classical Mechanics
1. What is the circumference of a circle with a radius of 2.1 cm? your answer as a number; do not include units. You must use the appropriate number of significant figures.
2. Density is defined as mass per unit volume. A solid cylinder has a diameter of 17.4 mm and a length of 50.3 mm. Its mass is 49 g. What is its density? Give your answer in metric tonnes per cubic metre. (The metric tonne is 1000 kg.) Write your answer as a number, using the appropriate number of significant figures.
3. A solar racing car* typically has a power of about 1.2 kW (1.2 kilowatts). What is this in horsepower (hp)? (Use the conversion 1 hp = 745.7 watts). Give your final answer as a number, with the appropriate number of sig figs.
4. Absolute value of vector A = Absolute value of vector B = Absolute value of vector C. Further, Vector A+ Vector B +Vector C = 0. What is the angle between vector A and Vector B?
Express your answer in degrees.
2. Density is defined as mass per unit volume. A solid cylinder has a diameter of 17.4 mm and a length of 50.3 mm. Its mass is 49 g. What is its density? Give your answer in metric tonnes per cubic metre. (The metric tonne is 1000 kg.) Write your answer as a number, using the appropriate number of significant figures.
3. A solar racing car* typically has a power of about 1.2 kW (1.2 kilowatts). What is this in horsepower (hp)? (Use the conversion 1 hp = 745.7 watts). Give your final answer as a number, with the appropriate number of sig figs.
4. Absolute value of vector A = Absolute value of vector B = Absolute value of vector C. Further, Vector A+ Vector B +Vector C = 0. What is the angle between vector A and Vector B?
Express your answer in degrees.
Classical Mechanics
Three objects are connected on a table as shown in the Figure.
The coefficient of kinetic friction between the block of mass m2
and the table is 0.350. The objects have masses of m1 = 4.00 kg,
m2 = 1.00 kg, and m3 = 2.00 kg, and the pulleys are frictionless.
(a) Draw a free-body diagram of each object. (b) Determine the
acceleration of each object, including its direction. (c) Determine
the tensions in the two cords. What If? (d) If the tabletop were
smooth, would the tensions increase, decrease, or remain the
same? Explain.
The coefficient of kinetic friction between the block of mass m2
and the table is 0.350. The objects have masses of m1 = 4.00 kg,
m2 = 1.00 kg, and m3 = 2.00 kg, and the pulleys are frictionless.
(a) Draw a free-body diagram of each object. (b) Determine the
acceleration of each object, including its direction. (c) Determine
the tensions in the two cords. What If? (d) If the tabletop were
smooth, would the tensions increase, decrease, or remain the
same? Explain.
Classical Mechanics
Q1.Find the direction and magnitude of an electric field that exerts a 4.8×10*17N westward force on an electron
b. What magnitude and direction force does this field exert on a proton
b. What magnitude and direction force does this field exert on a proton
Classical Mechanics
Q1.a) Find the direction and magnitude of an electric field that exerts a westward force on an electron.b) what magnitude and direction force does this field exert on a proton
Q2. An electron gun has parallel plates separated by 4.00cm and gives electrons 25.0KeV of energy
a) what is the electric field strength between the plates. b)what force will this field exert on a piece of plastic with a 0.500μF charge that gets between the plates?
Q3. Find the total capacitance of the combination of capacitors. C1=1μF C2 =5μF C3=8 μF
Q2. An electron gun has parallel plates separated by 4.00cm and gives electrons 25.0KeV of energy
a) what is the electric field strength between the plates. b)what force will this field exert on a piece of plastic with a 0.500μF charge that gets between the plates?
Q3. Find the total capacitance of the combination of capacitors. C1=1μF C2 =5μF C3=8 μF
Classical Mechanics
(7) As a car of mass m kg drives up a slope at an angle α to the horizontal it experiences a
constant resistive force FN and a driving force D N.What can be deduced about the work
done by D as the car moves a distance d metres uphill if:
(i) the car moves at constant speed?
(ii) the car slows down?
(iii) the car gains speed?
The initial and final speeds of the car are denoted by um/s and vm/s respectively.
(iv) Write v
2
in terms of the other variables.
constant resistive force FN and a driving force D N.What can be deduced about the work
done by D as the car moves a distance d metres uphill if:
(i) the car moves at constant speed?
(ii) the car slows down?
(iii) the car gains speed?
The initial and final speeds of the car are denoted by um/s and vm/s respectively.
(iv) Write v
2
in terms of the other variables.
Classical Mechanics
A projectile of mass 56kg is moving at a constant speed of 8 m/s when it explodes into three pieces A, B and C. A(20 kg) flies along at 20 m/s along the line of flight and B(16 kg) flies at 15 m/s at 45 degrees to the line of flight in the forward direction. Find the velocity of mass C in magnitude and direction and estimate the energy supplied in the explosion.
