Yacht Rope
Urgent Physics Help PLEASE!!?
Could people help me answer these problems please? I know it’s a hassle but I’m really lost. There must be at least one expert out there… All help will be very much appreciated!! =D Oh and it would be helpful if you can show me how u got to the answer.
1. Why is it easier to pull a sled with a 2m rope than it is to push it with a 2m pole? (Assume both rope and pole are at the same angle to the ground’s surface)
2. A ship sails 10km on a bearing of 320 degrees. What are the components of its displacement to the EAST?
3. Two forces of 80N and 100N acting at an angle of 60 degrees with each other, pull on an object. What is the size of the single pull that would replace the given forces? (Solve by vector diagram)
4. A yacht is sailing due North at 7ms-1 and the wind is blowing West at 4ms-1. What is the wind’s velocity relative to the yacht’s sail?
Thank you!!
1) A rope is lighter than a pole, so it reduces the amount of work required to move the lighter sled. (I’m not sure if this answer is correct.)
2) 320 degrees bearing is the same as 40 degrees west of north. So If you draw a vector of 10 km in that direction, the x component is x = – (10 km)sin(40) = -6.43 km.
You can also change the angle to the polar form. measured CCW from the +x axis. You get: 130 degrees. So:
x = (10 km) cos(130) = -6.43 km. Again, the negative means to the left. So the components of displacement to the east are negatve (-6.43 km).
3)
First draw a vector diagram of the forces. Basically, draw a triangle ABC (not to scale – but if it can somewhat resemble the actual proportions that would be better).
Let AB = the 100 N force (point in the direction of A to B).
then BC is the 80 N force
Vector AC is the resultant (single) force.
Extend AB (as a ray and put a point D on that extension)
then angle CBD is 60 degrees.
(so angle CBA = 180 – 60 = 120 degrees)
Now using the cosine law (which is:
c² = a² + b² – 2ab*cos(θ),
where c is the length of the side you want to find (two of the sides are 80 and 100 N, so c is the remaining side); a and b are the two sides (80 and 100); and θ is the angle between a and b (between 80 and 100 N vectors).
When you solve for c, you get the magnitude of the resultant force. All that’s needed is the direction, which can be found by finding either of the two unknown angles. You will require sine law:
sin(A) /a = sin(B) / b = sin(C) / c
So where a is the side opposite angle A, b is the side opposite B, etc.
(4)
Draw it out again: its gonna be a right triangle. Draw a vector that goes 7 units upward, continue from up there another vector that goes 4 units left (wind speed), and connect the original vector (the tail of it) to the tip of the second vector. You should have a right triangle with legs 7 and 4, you can find the hypotenuse, and the angles using trig.
Sorry for being wordy and not making sense. Its late night and i’m really tired… In fact i’m gonna crash now….
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