mechanics questions help plss!!!

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luce1411
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#1
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hii I'm really struggling with these questions we got set for homework. can anyone help out with these alevel mechanics questions?? literally my last hope 😭

1 A rough plane is inclined to the horizontal at an angle a, where tan a = 3/4. A brick P of mass m is placed on the plane.
The coefficient of friction between P and the plane is mu
Brick P is in equilibrium and on the point of sliding down the plane.
Brick P is modelled as a particle. Using the model
(a) find, in terms of m and g , the magnitude of the normal reaction of the plane on brick P ( b) show that mu = 3/4

2 A particle P moves with acceleration (4i - 5j) ms - 2
At time t = 0 , P moving with velocity (- 2i + 2j)ms-1
(a) Find the velocity of at time t = 2 seconds.

3 At time t seconds , where t >= 0 , a particle P moves so that its acceleration a ms-2 is given by
a = (1 - 4t) i + (3 - t ^ 2) j
At the instant when t = 0 , the velocity of P is 36i ms-1
(a ) Find the velocity of P when t = 4

much appreciated yall 😽✌️
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ZR2002
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for 1- you know that the normal reaction is equal to mgcos a and you can use inverse tan a to get a then put it into cos to get an answer. for part b you know that mgsina is equal to friction as the particle is in equillibrium so you know that mu x normal reaction is equal to mgsina. so you rearrange to find mu
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ZR2002
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2 A particle P moves with acceleration (4i - 5j) ms - 2
At time t = 0 , P moving with velocity (- 2i + 2j)ms-1
(a) Find the velocity of at time t = 2 seconds.

for this one, you use v=u+at. u is (- 2i + 2j)ms-1, you have a and you put in t=2 to get v
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ZR2002
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3 At time t seconds , where t >= 0 , a particle P moves so that its acceleration a ms-2 is given by
a = (1 - 4t) i + (3 - t ^ 2) j
At the instant when t = 0 , the velocity of P is 36i ms-1
(a ) Find the velocity of P when t = 4

same thing here i think but you have a, t and u so you do u+ at to get v .
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luce1411
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hii thank you so much for your help I'm super grateful!! do you think you could help with these 2 questions as well? would be much appreciated

A ladder AB has mass M and length 6a.

The end A of the ladder is on rough horizontal ground.

The ladder rests against a fixed smooth horizontal rail at the point C.

The point C is at a vertical height 4a above the ground.

The vertical plane containing AB is perpendicular to the rail.

The ladder is inclined to the horizontal at an angle a, where sin a= 4/5,, as shown in Figure 1.

The coefficient of friction between the ladder and the ground is u.


The ladder rests in limiting equilibrium.

The ladder is modelled as a uniform rod.

Using the model,

(a) show that the magnitude of the force exerted on the ladder by the rail at C is 9Mg/25

(6) Hence, or otherwise, find the value of mu.



A small ball is projected with speed Ums from a point O at the top of a vertical cliff.
The point is 25 m vertically above the point N which is on horizontal ground.
The ball is projected at an angle of 45° above the horizontal.
The ball hits the ground at a point A, where AN= 100 m, as shown in Figure 2.
The motion of the ball is modelled as that of a particle moving freely under gravity.
Using this initial model,
(a) show that U28

(b) find the greatest height of the ball above the horizontal ground NA.

In a refinenment to the model of the motion of the ball from O to A, the effect of air
resistance is included.

This refined model is used to find a new value of U.
(c) How would this new value of U compare with 28, the value given in part (a)?

(d) State one further refinement to the model that would make the model more realistic.
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YuvrajRam
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(Original post by luce1411)
hii thank you so much for your help I'm super grateful!! do you think you could help with these 2 questions as well? would be much appreciated

A ladder AB has mass M and length 6a.

The end A of the ladder is on rough horizontal ground.

The ladder rests against a fixed smooth horizontal rail at the point C.

The point C is at a vertical height 4a above the ground.

The vertical plane containing AB is perpendicular to the rail.

The ladder is inclined to the horizontal at an angle a, where sin a= 4/5,, as shown in Figure 1.

The coefficient of friction between the ladder and the ground is u.


The ladder rests in limiting equilibrium.

The ladder is modelled as a uniform rod.

Using the model,

(a) show that the magnitude of the force exerted on the ladder by the rail at C is 9Mg/25

(6) Hence, or otherwise, find the value of mu.



A small ball is projected with speed Ums from a point O at the top of a vertical cliff.
The point is 25 m vertically above the point N which is on horizontal ground.
The ball is projected at an angle of 45° above the horizontal.
The ball hits the ground at a point A, where AN= 100 m, as shown in Figure 2.
The motion of the ball is modelled as that of a particle moving freely under gravity.
Using this initial model,
(a) show that U28

(b) find the greatest height of the ball above the horizontal ground NA.

In a refinenment to the model of the motion of the ball from O to A, the effect of air
resistance is included.

This refined model is used to find a new value of U.
(c) How would this new value of U compare with 28, the value given in part (a)?

(d) State one further refinement to the model that would make the model more realistic.
hi, did u manage to work this out as im also having trouble with the same question.
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