Momento Mistaki Mechanics

Why does standing on the base of a ladder stop it from slipping?

Reaction at wall is unchanged (show with moments about floor)

Reaction at floor increases

which increases max F available

Suggest two improvements that could be made to the model (stones thrown off cliff) g = 10ms^-2

Include Air resistance

Include wind effects

use a more accurate value for g

include dimensions of the stones

(in the model of the motion

[for P where the coefficients of the downhill component of the weight and the friction are equal and Q is the same but with a greater mass] explain briefly why Q will remain at rest on the plain

The forces acting on Q will still balance as the m’s cancel

OR the friction will increase in the same proportion as the weight component or force down the plane

[A brick has an equation such that the weight component down the plane is always equal to the friction. Brick is projected with speed 0.5 down a line of greatest slope of the plane, modelled as particle.] Using the model describe the motion of brick giving a reason for your answer.

Brick Q slides down the plane with constant speed. no resultant force so no acceleration.

don’t forget when finding the greatest height above ground of a ball thrown from a ledge

The height of the ledge

in a refinement to the model of motion of the ball from O to A, the effect of air resistance is included and this refined model is used to find a new value of U. How would this new value of U compare 28, the value given in part a

New value > 28

State one further refinement [other than air resistance] to the model that would make the model more realistic

ind effects, more accurate value of g, spin of ball, include size

of the ball, not model as a particle, shape of ball

“Write down an equation of motion for a” how far do you go?

F and T and trigcomponent = ma

Sketch a velocity time graph for B (b is connected to a and a has acceleration of a constant) explaining your answer

straight line because acceleration of b is constant

(connected particles over a pulley) “In reality, the string is not light. State how this would affect the working (that combines the equation of motion of A and B, cancelling T)

the tensions in the two equations of motion would be different.

Tension on A would be different to tension on B

when you have a ladder with rough ground but a smooth wall and you’ve found the reaction at the wall in the first part but don’t know is Fr is limiting and then a force is applied towards the wall at the floor, how do you find the value of the force k that is applied and what do you include in your working for 5 marks? GIVEN THAT IT IS IN LIMITING EQUILIBRIUM

Must take moments about A AGAIN to get the SAME value of the reaction at the wall. Then friction will act away from the wall because reaction at wall is fixed so for Fr to be max must be away then solve for the singular value of K

If you have a particle moving from rest on a smooth surface and you have two forces, one of which has unknown coefficients, both in i and j form and you have the direction of motion, how do you make an equation for the unknown coefficients?

The direction of motion will be the same as the direction of force (acceleration) so you can sum the forces and use ratios, the ratio of x and y components for the resultant force and the direction of motion are equal. rearrange

how to find the length of AB when A is at rest and you have an equation for the resultant force on the particle and the time it is at B

Find a from the resultant force and use suvat.

Explain why the frictiol force acting on the rod at a [the rough ground] acts horizontally to the right [when the only other force is tension in a diagonal string attached to the other end of the rod]

The horizontal component of T acts to the left and since the only

other horizontal force is friction, it must act to the right oe

if you have U sina = b and U²sinacosa = c how to find U²

divide c by b to get Ucos a = d then: Square both equations [cosa and sina], factor out sin²a+cos²a and so U² = b²+d²

when air resistance is taken into account and the distance travelled by a ball is the same which of the ORIGINAL U or NEW V initial velocity will be greater? ‘State which is greater, giving a reason for your answer’

V , since air resistance has to be overcome, or just ‘because of air

resistance’

If S is the reaction for at the smooth wall and the only other horizontal force on a ladder is friction and the only other force apart from that at the ground is its weight and the centre of gravity moves closer to the wall “State whether this new value for S is larger, smaller or equal to the value that S would take using the inital model [where the rod is uniform] Give a reason for your answer”

New value of S would be larger as the moment of the weight about A

would be larger

If S is the reaction for at the smooth wall and the only other horizontal force on a ladder is friction '‘state the direction of the frictional force acting on the rod at the ground

The normal reaction at B is acting to the left so it must act to the right,

right as it needs to balance (oppose, counter) the force at B, right as it

prevents the rod from sliding (slipping, falling), right as the weight (mass)

of the rod will mean the rod tends to slip left, mass or weight will be

pushing the rod to the left so friction will oppose that.

Speed as a surd yes or no? 2023

yes

time as 3/2 yes or no 2023

no. 1.5

Coefficient of friction as fraction yes or no? 2023

yes

With lift questions what force is exerted on the lift by the person

a reaction force that is equal to that experienced by the person FROM the lift

In lift questions what are the forces on the lift?

The force exerted on the lift by the person, The tension in the cable, the weight of the lift

In lift questions what are the forces on the person

the force exerted by the lift on the person (reaction force) and persons weight

Is the normal reaction force in an accelerating lift equal and opposite to the persons weight?

No because the lift is accelerating. If accelerating upwards it is greater than the weight.

How to think of the normal reaction forces between the lift and person?

Like the tension in a cable between them. They cancel out when considering the whole system

In lift problems what are the forces on the whole system

The weight of the lift and its contents. The tension in the string. any ADDITONALLY added forces from the question (resistance etc)

How does thrust act?

Opposite to tension - out!

Should the speed from a VT graph be left in exact form 2024

seems so

State what would happen to a particle if [coefficient of friction was such that the acceleration DOWN the slope was less than or equal to 0 for only friction and weight]

p would not move

How to make a quadratic model for a projectiles question

consider vertical and horizontal motion at ANY point labelling the distances as x and y and combine with the common T’s

The model is refined to include air resistance. state which is greater [the new greatest height or the old one], justifying your answer

old is greater (or new is smaller), as air resistance would slow the particle

down oe

Explain why velocity time graphs were the only motion is constant acceleration, where one starts from a velocity and the other from rest but two seconds later, must cross before they get get to T where T is the time when they meet in space “explain why the two graphs must cross before time t =T seconds

Lines must cross before time T seconds, since area under each graph

must be equal

In reality the rope would not be light. “state how this would affect the tension in the rope”

The tension would not be constant oe

When you have a projectiles question and you have it in terms of i and j vectors and it says the inital velocity is V “find the value of V” what do they want?

The speed (no direction needed)