PHYSICS: motion, momentum, force, work, energy, heat
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| Isaac Newton (1643-1727) |
[1] Momentum of a moving object:
p = mv i.e. momentum = mass × velocity. p
is momentum, m is mass and v is velocity.
Question: calculate the momentum of a 7 kg tenpin bowling ball travelling
at a speed of 2.5 m/s. (Answer is 17.5 kg m/s)
[2] Force and momentum:
force = (change of momentum) / time.
Question: A golf ball has a mass of 0.046 kg. After being
struck by a golf club, it leaves the tee at a speed of 60 m/s. Calculate (a)
the change in momentum of the golf ball and (b) the force exerted on the ball
if the golf club is in contact with the ball for a time of 4.0 × 10-4
s.
[3] Speed of a satellite in circular
orbit: (circumference of orbit) / (period T of orbit)
[This formula actually applies to any object moving
in a circle at constant speed - not just satellites.
Question: see below.
[4] Centripetal force : F = mv²/r,
where m is the mass, v is the orbital velocity and r is the radius of orbit.
Since F = ma, the centripetal acceleration is given by a
= v²/r.
Question: Here is some data about a surveillance satellite in orbit:
radius of orbit = 7.1 × 106 m; speed of satellite = 7.5 ×
103 m/s; mass of satellite = 1.2 × 103 kg. Calculate
(a) the orbital time of the satellite (b) the centripetal acceleration of
the satellite and (c) the value of the unbalanced force that acts on it. (Answer
is (a) 5.9 × 103 s (b) 7.9 m/s2 and (c) 9.5 ×
103 N)
[5-8] Equations of motion:
| v = u + at | v² = u² + 2as | s = ut + ½at² | s = ½(u + v)t |
where u is the initial velocity, v is the final velocity, t is the time of
motion, s is the displacement and a is the acceleration. [These apply for
bodies moving with constant acceleration.]
Question: A bicycle travelling at 6 m/s increases its speed to 12
m/s in 12.0 s. Calculate its acceleration and the distance it travels while
it is accelerating. (Answer is 0.5 m/s2 and 108 m.)
[9 & 10] Hooke's Law:
"the extension of a spring or wire is proportional to the force, provided
that the limit of proportionality is not exceeded", or force
is proportional to extension, i.e. F = kx where
F is the force, k is the spring constant and x is the extension.
Question: A 15 N weight stretches a spring by 0.22 m. Calculate the
spring constant. (Answer is 68.18 N/m)
Also: Energy stored in a spring: E = ½Fx
Question: A 15 N weight stretches a spring by 0.22 m. Calculate
the energy stored in the stretched spring. (Answer is 1.65 J)
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| Anders Celsius (1701-1744) |
[11] Heat energy transfer: E = m ×
c × Δθ, i.e. heat transfer
= mass x specific heat capacity x temperature change, where m is
the mass, c is the specific heat capacity and Δθ
is the temperature change (measured in K or °C).
[When heated, materials get hotter because of the increased movement of their
molecules.]
Question: a kettle is filled with 1.50kg of water at a temperature
of 10°C. The kettle is switched on until the water boils at 100°C.
Calculate the energy absorbed by the water, if the specific heat capacity
of water is 4.2 × 103 J/kg°C. Answer: 5.67 ×
105 J.
*** The following gas formula is only needed for the Edexcel and OCR syllabus. ***
[12] Gas pressure and temperature: P1/T1
= P2/T2, where P is the pressure and T is the
Kelvin temperature (the Kelvin temperature is the Celsius temperature minus
273.) and k is a constant.
[Gases consist of large numbers of particles moving constantly and randomly,
changing speed and direction as they collide. Gas pressure is a result of
the forces exerted when the particles collide with the walls
of the container.]
Question: the pressure of a gas in a cylinder is 3.5 × 10 Pa
when the temperature is 20°C. Calculate the pressure of the gas at a temperature
of 50°C.
Answer: 3.9 × 105 Pa.
