MOVING
ABOUT WORKSHEETS
VECTOR ANALYSIS
WORKSHEET No.1
Answers
are supplied. Simply click on the word "answers" at the end of
each question.
1.
A ship is heading due west at a steady speed of 15 km/h.
A current of 3 km/h is running due south.
Calculate the velocity of the ship relative to the seabed.
(Hint: The velocity of the ship plus the velocity of the current will add
up to the total velocity of the ship relative to the seabed.) Answers
2.
Two tractors pull on a large boulder in an effort to shift it out of the
way of a new fence line. One
tractor pulls with a force of 3000 N west and the other tractor pulls with a
force of 2500 N in a southerly direction because of the terrain.
Determine the resultant force acting on the boulder.
If the boulder has a mass of 1000 kg calculate the acceleration of the
boulder due to the resultant force acting on it. Answers
3.
Three coplanar horizontal forces each of magnitude 10 N act on a body of
mass 5 kg as shown below. Determine
the magnitude of the net force acting on the body and the magnitude of the
resultant acceleration. Answers
4.
If vector A = 5 N north and vector B = 10 N east, find the resultant of
vector A – vector B. Answers
5.
A submarine is travelling at 20 km/h due east.
A short time later it is travelling due north at 15 km/h.
Calculate the change in velocity of the submarine. Answers
6.
An F117A Nighthawk stealth fighter jet has a true airspeed of 1000 km/h due east.
There is a cross wind blowing in a direction E60^{o}S at 100
km/h. Calculate the velocity of the
jet relative to the ground. (Hint:
You will need to use the cosine & sine rules if you intend to do this
question mathematically.) Answers
7.
A sled of mass 10 kg sits on a horizontal surface as shown below.
A force is exerted on the sled by means of a rope inclined at 60^{o} to
the horizontal. If the tension in
the rope is 150 N and the frictional force between the sled and the horizontal
surface is 55 N, will the sled move under these conditions?
Explain. If the sled does
move determine the size of the acceleration with which it moves. Answers
8.
A barge of total mass 300 kg is pulled by a single rope attached to a
tugboat of mass 1000 kg. If the
drag on the tug and the barge is onetenth of their respective weights, and the
total forward force exerted by the tug is 5130 kg force (ie 5130 x 9.8 N), find
the magnitude of:
a.
the total force resisting the forward motion of the tug and barge;
b.
the acceleration of the tug/barge system;
c.
the unbalanced accelerating force on the barge;
d.
the tension in the towing rope.
Answers
9.
An astronaut of mass M_{A} = 80 kg stands on the
horizontal floor of a spaceship moving vertically with acceleration a.
If the acceleration due to gravity on the astronaut is g
= 9.8 ms^{2}, write a mathematical expression for and calculate the
value of the reaction force R between the astronaut and the floor of the spaceship when:
a.
a = 0;
b.
a = 8 ms^{2}
upwards;
c.
a = 8 ms^{2}
downwards.
Answers
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ANSWERS TO VECTOR ANALYSIS
WORKSHEET No.1
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questions.
1.
15.3 km/h W11.3^{o}S or S78.7^{o}W
2.
Resultant force = 3905 N in a direction of W39.8^{o}S &
acceleration = 3.9 ms^{2} in the same direction as the resultant force.
3.
Net force = 20 N & resultant acceleration = 4 ms^{2}.
4.
11.2 N in a direction of N63.4^{o}W
5.
25 km/h in a direction of N53.1^{o}W
6.
1054 km/h E5^{o}S
7.
Horizontal force to the left on sled is 75 N, which is greater than the
friction force to the right. Therefore
the sled will move to the left with an acceleration of 2 ms^{2}.
If you did not get the right acceleration, ask yourself how much of the
75 N to the left actually accelerates the sled – all of it or just some of it?
Some of it has to overcome friction!
8.
(a) 1274 N, (b) 37.7 ms^{2}, (c) 11 307 N, (d) 11 601 N.
9.
(a) R = M_{A} g =
784 N upwards; (b) R = M_{A} g +
M_{A} a
= 1424 N upwards; (c) R
= M_{A} g
 M_{A} a = 144 N upwards.
Return to Vector Analysis
Worksheet No.1
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FORCE
– WORKSHEET 1
Note: For full solutions to
this worksheet see the pdf file at the end of the questions.
ENERGY
 WORKSHEET 1
MOMENTUM
– WORKSHEET 1
MOMENTUM
– WORKSHEET 2
REVISION WORKSHEET No.1
1.
Kate is chasing Angela with a large bucket of water.
She runs 100m due east, followed by 100m due north and then 150m due
south. Calculate Kate’s
displacement from her start point at the end of her run. Answers
2.
Brad’s Lamborghini has an initial velocity of 20ms^{1} south
and an acceleration of 5 ms^{2} south for five seconds.
Determine:
a.
the total change in velocity of the car
b.
the final velocity of the car after five seconds.
Answers
3.
A car changes its velocity from 5 ms^{1} south to 12 ms^{1}
east. Calculate the change in
velocity of the car. Answers
4.
A car of mass 1000kg changes its velocity from 20ms^{1} north to
30ms^{1} north in 2 seconds.
a.
Determine the amount of work done by the engine of the car to achieve
this change in velocity.
b.
Calculate the acceleration of the car and the net force applied by the
engine to cause this acceleration.
Answers
5.
A truck of mass 5000kg travelling at 15ms^{1} is brought to rest
in a distance of 100m.
a.
Calculate the average force exerted by the truck’s brakes to achieve
this change in velocity.
b.
Identify the energy transformations that occur as the truck’s kinetic
energy is reduced to zero.
Answers
6.
A bus travels at constant speed of 12ms^{1} around a circular
bend of radius 150m.
a.
Determine the centripetal acceleration (magnitude & direction) of the
bus as it negotiates the bend.
b.
Calculate the centripetal force acting on the bus (magnitude &
direction), if the mass of the bus is 2000kg.
Answers
7.
A ship is heading due west at a steady speed of 15 km/h.
A current of 3 km/h is running due south.
Calculate the velocity of the ship relative to the seabed.
(Hint: The velocity of the ship plus the velocity of the current will add
up to the total velocity of the ship relative to the seabed.) Answers
8.
Two trucks pull on a large boulder in an effort to shift it out of the
way of a new fence line. One truck
pulls with a force of 3000 N east and the other truck pulls with a force of 2500
N southeast.
a.
Determine the magnitude of the net force acting on the boulder.
(Hint: A scaled vector diagram would be helpful here.)
b.
If the boulder has a mass of 500 kg calculate the size of the
acceleration of the boulder due to this net force.
Answers
9.
Two railway cars are being used in a structure integrity test.
Car A of mass 900 kg moves east at 25 ms^{1} and collides but
does not coalesce with Car B of mass 700kg moving west at 20 ms^{1}. After collision Car B is moving east with a speed of 30.6 ms^{1}.
Determine:
a.
The total momentum of the system before collision.
b.
The total momentum of the system after collision.
c.
The speed and direction of Car A after collision.
d.
The change in momentum of Car A as a result of the collision.
e.
The average force acting on Car A, given that the change in momentum took
1.5 seconds.
Answers
10.
Study the graph below, which shows the velocity of a vehicle over a
period of time.
Determine:
a.
The average speed of the vehicle from t = 2s to t = 4s.
b.
The instantaneous speed of the vehicle at t = 3s.
c.
The acceleration of the vehicle from t = 2s to t = 4s.
d.
The total distance covered from t = 0 to t = 4s.
Answers
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ANSWERS TO REVISION
WORKSHEET No.1:
Just use your browser's back
button to return to the
questions.
1.
111.8m E26.6^{o}S
2.
(a) 25ms^{1} South; (b) 45ms^{1} South
3.
13ms^{1} E22.6^{o}N
4.
(a) 2.5 x 10^{5} J; (b) 5ms^{2} north and
5000N north.
5.
(a) 5625N in opposite direction to original motion; (b) kinetic
energy is transformed into sound & heat energy.
6.
(a) 0.96ms^{2} towards centre of circular bend; (b)
1920N in same direction as the centripetal acceleration.
7.
15.3 km/h W11.3^{o}S (or S78.7^{o}W)
8.
(a) 5000N; (b) 10ms^{2}
9.
(a) 8500Ns East; (b) 8500Ns, East; (c) 14.35ms^{1}
West; (d) 35 415Ns, West; (e) 23 610N, West.
10. (a)
2ms^{1}; (b) 1.8ms^{1}; (c) 2ms^{2} in opposite
direction to motion; (d) 12m.
