Transcript Work, power & energy - questions & solutions

Work, power and energy(2)
Solutions
AQUINAS DIOCESAN GRAMMAR
Q1. A pole-vaulter has a mass of 50kg.
(a) What is her weight in newtons?(g = 10N/kg)
W = mg
= (50)(10) = 500N
(b) If she vaults to 4 m high, what is her
gravitational potential energy?
P.E. = mgh
P.E. = (50)(10)(4)
= 2000J
AQUINAS DIOCESAN GRAMMAR
(c) How much kinetic energy does she have just
before reaching the ground?
P.E. at top = K.E. at bottom
K.E. just before reaching the ground – 2000J
AQUINAS DIOCESAN GRAMMAR
Q2. A car of mass 1000kg is travelling at 30m/s.
(a) What is its kinetic energy?
K.E. = ½ mv2
=½ (1000)(30)2 = 450000J
(b) If slows to 10m/s. What is its K.E. now?
K.E. = ½ mv2
=½ (1000)(10)2 = 50000J
AQUINAS DIOCESAN GRAMMAR
Q2.
(c) What is the change in kinetic energy?
Change in K.E. = Initial K.E. – Final K.E.
= 450000 – 50000 = 400000J
(d) If it takes 80m to slow down by this amount,
what is the average breaking force?
Work Done = Change in energy = Force x Distance
400000 = Braking Force x 80
Average Breaking force = 400000  80 = 5000N
AQUINAS DIOCESAN GRAMMAR
Q3. A girl throws a ball upwards at a velocity of
10m/s. How high does it go?(g = 10N/kg)
K.E. at bottom = P.E. at top
½ mv2 = mgh
½ (10)2 = 10h
h = 5m
AQUINAS DIOCESAN GRAMMAR
Q4. An electric lamp is marked 100W. How
many joules of electrical energy are tranformed
into heat and light,
(a) during each second.
100W = 100J/s
100J of energy converted every second
(b) During a period of 100s.
No. of joules during 100s = 100 x 100
= 10000J
AQUINAS DIOCESAN GRAMMAR
Q5. Calculate the kinetic energy of a sprinter of
mass 60kg running at 10m/s.
K.E.sprinter = ½ mv2
= ½ (60)(10)2
= 3000J
AQUINAS DIOCESAN GRAMMAR
Q6. A free-wheeling motor cyclist of mass
(including her machine) 100kg is pushed from
rest over a distance of 10m. If the push of 250N
acts against a frictional force of 70N, calculate
the kinetic energy and velocity when the push
ends.
70N
m =100kg
200N
Resultant Force = 250 - 70 = 180N to the right
Work Done = Force x Distance = Energy Changed
= 180 x 10 = 1800J (KE when push ends)
AQUINAS DIOCESAN GRAMMAR
Solution Q6 contd.
KE when the push ends is 1800J
K.E. = ½ mv2
1800 = ½ (100)v2
v = ((1800 x 2)  100)
= 6 m/s
Velocity when push ends = 6m/s
AQUINAS DIOCESAN GRAMMAR
Q7. A grandfather clock uses a mass of 5kg to
drive its mechanism. Calculate the gravitational
potential energy stored when the mass is
raised through its maximum height of 0.8m.
P.E. = mgh
= (5)(10)(0.8)
= 40J
AQUINAS DIOCESAN GRAMMAR
Q8.
(a) What is the velocity of an object of mass 1kg
which has 200J of K.E.?
K.E. = ½ mv2
200 = ½ (1)v2
v2 = 400
v = 20m/s
AQUINAS DIOCESAN GRAMMAR
Q8.
(b) Calculate the p.e. of a 5kg mass when it is
(i) 3m, (ii) 6m, above the ground. (g = 10N/kg)
(i) P.E. = mgh
P.E. = (5)(10)(3)
= 150J
(ii) P.E. = mgh
P.E. = (5)(10)(6)
= 300J
AQUINAS DIOCESAN GRAMMAR
Q9. A 100g steel ball falls from a height of 1.8m
on to a plate and rebounds to a height of 1.25m.
Find
(a) the PE of the ball before the fall (g=10m/s2)
M = 100g = 0.1kg
1.8m
1.25m
PEtop = mgh
PE = (0.1)(10)(1.8)
= 1.8J
AQUINAS DIOCESAN GRAMMAR
Q9. (b) the KE as it hits the plate,
M = 100g = 0.1kg
PEtop = KEbottom
KE = 1.8J
1.8m
1.25m
AQUINAS DIOCESAN GRAMMAR
Q9. (d) the KE as it leaves the plate on the
rebound,
M = 100g = 0.1kg
1.8m
rebounds
1.25m
Petop = KEbottom
rebounds to 1.25m
Energy at bottom =mgh
= (0.1)(10)(1.25)
= 1.25J
AQUINAS DIOCESAN GRAMMAR
Q9. (e) its velocity on rebound,
M = 100g = 0.1kg
½(0.1)v2 = 1.25
V = 5m/s
1.8m
rebounds
1.25m
AQUINAS DIOCESAN GRAMMAR
Q10. A body of mass 5kg falls from rest and has
a KE of 1000J just before touching the ground.
Assuming there is no friction and using a value
of 10m/s2 for the acceleration due to gravity,
calculate
(a) the loss of PE during the fall.
Loss in PE = Gain in KE
Gain in KE = 1000J
AQUINAS DIOCESAN GRAMMAR
Q10. (b) the height from which the body has
fallen.
PEtop = mgh
1000 = (5)(10)h
h = 20m
AQUINAS DIOCESAN GRAMMAR