Forces
Velocity
Dot Product
Cross Product
Applications
100
A single force that opposes the resultant force, and keeps the object in a state of equilibrium.
What is an equilibrant force?
100
What is the formula for speed?
V = d /t
100
If the dot product between two vectors is negative, then the angle between the two vectors is...
obtuse
100
What is the formula for cross product?
a x b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)
100
Calculate the work done, by a box pushed 50 m, by a 20 N force at an angle of 30 degrees to the ground.
866 J
200
F1 has a magnitude of 6N west, F2 has a magnitude of 12 N south; Find the resultant force. (Don’t forget direction).
Resultant = root 180 N, 63 degrees south of west
200
A jet is travelling north with a speed of 500 km/h. It encounters a wind from the east at 45 km/h. How far will the jet have travelled in two hours, and in what direction?
502 km / h, 85 degrees north of west, distance = 1004 km in 2 hours
200
Name and explain the 4 properties of dot product.
1) Distributive Property 2) Commutative Property 3) Magnitudes Property 4) Associative Property with scalar
200
Which of the following calculations are meaningless? 1) (a . b) x c 2) (a x b)c 3) 3) (a+b) + c
1 IS MEANINGLESS
200
A particle is moved from A (3, 5) to B (5, 10) by a 10 N force that acts 50 degrees to AB. Calculate the work done.
34.6 J
300
Find the Horizontal and vertical components of a force of 80 N, 80 degrees above the horizontal axis.
X component: 13.9 N Y component: 78.8 N
300
A boat is sailing at 40km /h in a direction of N 45 degrees W. It encounters a wind from E 15 N at a speed of 10km/h. Calculate the resultant velocity.
45.1 km/h (33 degrees north of west)
300
The dot product of a.b. gives a value of 15. The magnitude of a is 4, and the magnitude of b is 20. Calculate THETA.
Theta = 79 degrees
300
Name and explain the 3 properties of the cross product.
1) anti - commutative 2) distributive law 3) scalar law
300
Determine the area of the parallelogram, whose sides are determined by a (-1, 5, 6) and b (2, 3,-1)
Root 819 units squared
400
A 30 kg object is held up to the ceiling by two pieces of rope, one making an angle of 40 degrees with the ceiling, and the other making an angle of 50 degrees with the ceiling. Calculate the tension in each rope.
50 degree rope: 225.2 N, 40 degree rope: 189 N
400
Harman can swim at 5m/s in still water. She wishes to cross a river to a point directly opposite from where she is standing. The current has a speed of 3m/s downstream. At what angle relative to the shore should she swim?
53 degrees relative to the shore
400
Calculate the dot product of (4a – 3b) and (2a + b), when a = 5, b = 4, and the angle between a and b is 60 degrees.
132
400
Calculate the cross product of a (-2, -3, 5) and b (2, 4, 5)
(-35, 20, -2)
400
A 20 N force is applied to a wrench that is 20 cm long. The force makes an angle of 30 degrees with the wrench. Calculate the torque.
2 Nm
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