Essential Mathematics: Statics
27 flashcards · Mathematics · by lakesare
Name 3 Newton's laws of motion.
1. v doesn't change unless force is applied. In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.2. F = ma In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.3. Force by one body is met by equal opposing force. When one body exerts a force on a second body, the second body simultaneously…
Weight VS mass?
Weight is a force exerted on the object due to gravity. W = mg
If an object has a weight of magnitude 8N, what is its mass?
You can obtain a rough idea of the size of a newton by considering the masses, and hence the weights, of everyday objects. For example, a typical tomato has a mass of about 0.1 kg, so the magnitude of its weight is about 1 N. So if you place a tomato on your palm, then it will press down with a force of magnitude approximately one newton.
Describe tension forces present in this picture.
Any taut string exerts force at each of its 2 points of attachment. Each force: acts along the string directed away from the point of attachment Any taut string (or rope, wire or chain) exerts a tension at each of its two points of attachment. The tension at each point of attachment acts along the line of the string, and is directed away from the point of attachment. So, for example, the string in Figure 1 exerts an upward force on the 2 kg object, and a downward force on the hook. For a model…
Draw the force diagram (of forces acting on a mass).
The arrows represent the two forces that act on the object. The weight and the tension in the string are denoted by W and T, respectively, and the arrows are labelled accordingly.
[tricky notation, significant figures] Find the tension in the string that supports the 2 kg object. Give your answer in newtons to two significant figures.
Why is normal force called so?
Because normal force acts at right angles from the surface of the object. Whenever an object rests on a surface, there is a normal reaction of the surface on the object. This force acts at right angles to the surface. The word normal in ‘normal reaction’ means ‘at right angles’.
Find the component form of the following force. Assuming that i points to the right and j points up. The force F of magnitude 10 N that acts to the right and down at 30° to the vertical.
If θ is an acute angle in the right-angled triangle, the side opposite θ always has length |F|sinθ, and the side adjacent to θ always has length |F|cosθ. It's useful to remember this, to help you speed up your working.
Find the component form of the following force. Assuming that i points to the right and j points up. The force G of magnitude 6 N that acts to the left and down at 30° to the horizontal.
If θ is an acute angle in the right-angled triangle, the side opposite θ always has length |F|sinθ, and the side adjacent to θ always has length |F|cosθ. It's useful to remember this, to help you speed up your working.
How would you go about solving this?
P + R + Q = 0 (all are vectors) Resolve vectors in i and j directions Solve a system of equations So, to one decimal place, Q has magnitude 28.9 N and R has magnitude 57.7 N.
Choose directions for i and j and draw the force diagram.
Describe what happens in reality.
When the mass is not moving, the object experiences static friction. The friction increases as the applied force increases until the block moves. After the block moves, it experiences kinetic friction, which is less than the maximum static friction.
What does static friction depend on?
2 materials (expressed in μ static friction coefficient) how hard object is pressed against the surface (expressed in normal N) The static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: When there is no sliding occurring, the friction force can have any value from zero up to Fmax. Fmax attempting to slide one su…
[working with limiting static friction] A plastic box of mass 10 kg rests on a wooden floor. The coefficient of static friction between the box and the floor is 0.5. What is the maximum horizontal force that can be applied to the box without the box moving? Give your answer in newtons to two significant figures.
The maximum pushing force that can be applied without the box moving is 49 N.
What's the direction of the friction force? Draw the diagram.
One possibility is that the friction force and the tension in the string are both contributing to preventing the object from sliding down the plane. In this case, the friction force acts up the slope, as illustrated in the force (a). An alternative possibility, if the magnitude of the tension force is larger, is that the tension force may be ‘trying’ to pull the block up the plane, and the force of friction is preventing this from happening. In this case, the friction force acts down the slope,…
What's the link between these two equations? For the lamp: W1 + T1 = 0 For the aeroplane: W2 + T2 + T3 = 0 A child's bedroom ceiling lamp Force diagrams for the particles modelling the light and the model aeroplane
T1 = −T3. Forces T1 and T3 are different manifestations of the tension in the same string. Force T1 is the upwards force on the lower particle due to the upper particle, and Force T3 is the downwards force on the upper particle due to the lower particle. Since these forces are tensions in the same model string, they have the same magnitude but act in opposite directions. That is, T1 = −T3. Together, these two forces constitute an example of Newton’s third law of motion, which you met in the int…
For this situation - explain what's the manifestation of Newton's 3rd law. Two forces equal in magnitude and opposite in direction that act according to Newton’s third law are sometimes referred to as an action and an equal and opposite reaction.
Table exerts an upward force on object, object exerts a downward force of equal magnitude on table. It is important to appreciate that the two forces in Newton's third law act on different objects.NOT an action and an equal and opposite reaction:Weight of an object that rests on a surface and the normal reaction on the object from the surface (see the diagram).IS an action and an equal and opposite reaction: Table exerts an upward force on the object, object exerts a downward force of equal mag…
Prove that coefficient of static friction is a tangent of an angle where the object is at the point of slipping.
If you place an object on a plane - there's some angle α when it starts to slip. What does this angle α depend on? If you place an object on a plane and gradually increase the angle of inclination of the plane, then the angle α at which the object starts to slip does not depend on the mass of the object.
It only depends on coefficient of friction µ between these two materials. The angle α is given simply by α = tan−1µ, where µ is the coefficient of static friction between the object and the plane.
[Pyramids, includes friction, weight, normal, tension] The Egyptians of the time were unaware of the wheel and had no sophisticated machines, only human strength. It has been debated for many years just how each of these massive blocks of stone was raised up from the ground to its final position on the pyramid. There are no surviving records to give a definite answer to this question. One theory, backed by some archaeological evidence, is that the blocks were placed on sledges, attached to rope…
What's the difference between estimating n of workers needed to just hold the block at rest on the ramp pull it up?
just hold the block at rest on the ramp - the block is at the point of slipping down the slope, so the friction force acts up the slope. pull it up - friction force acts down the slope. You can use these facts to estimate the minimum number of workers needed to just hold the block at rest on the ramp, rather than pull it up, when friction is taken into account. In this situation the block is at the point of slipping down the slope, so the friction force acts up the slope. The normal reaction re…
Name 2 ways to solve it.
Find the tension in the cable by modelling aeroplane and light as 1 particle, and thus calculate the weight. Identify forces 1 by 1 An alternative approach is to first find the tension in the cable (the upper model string) by modelling all of the light, the model aeroplane and the string as a single particle of weight W1 + W2, and then find the tension in the string (the lower model string) by separately considering the model aeroplane and the string supporting it.
Draw the force diagram, and notice 4 equations and 4 unknowns. Two decorations hang from a string that is suspended at each end, as shown below. The left- and right-hand ends of the string make angles of 40◦ and 25◦ with the vertical, respectively, and the middle section is horizontal. The left-hand decoration has mass 0.95 kg.
In what situation is model pulley useful (apart from modelling an actual pulley)?
Where direction of the force is changed, but magnitude isn't. Pulley are useful for modelling any situation where the direction of a tension force changes, and friction where this change occurs is negligible. The key property of a model pulley, whether it models a real pulley or something else, is that it changes the direction of a tension force without changing its magnitude.
Draw the force diagram.
Draw the force diagram. After slipping from a mountain, a climber of mass 70 kg is suspended from a rope attached to another climber, of mass 75 kg, who stands on a ledge. The rope passes over a boulder on the edge of the ledge, and is horizontal between the standing climber and the boulder. If the boulder is modelled as a model pulley, what is the minimum coefficient of static friction between the soles of the standing climber’s boots and the top surface of the ledge that will stop the two cli…
Model the climbers as particles, the rope as a model string and the boulder as a model pulley. To find the minimum coefficient of static friction, assume that each climber is at rest, and the standing climber is at the point of slipping.
In what case does the coefficient of static friction µ = tan(α)?
???todo When the object is ready to move - in one direction or the other. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: When there is no sliding occurring, the friction force can have any value from zero up to Fmax. Fmax attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than Fmax overcomes the force…