Mechanics M1

[BurstBullet]

Hello!

These are a few questions regarding the Dynamics of Moving Particles:

1) A force of 20N is applied at an angle of 60(degrees) to the horizontal to a mass of 4kg on a smooth horizontal table. What is the acceleration of the mass? ans: 2.5ms^-2

2) A mass of 2kg is at rest on a rough horizontal table. A force of 20N is applied to the mass, the force making an angle of 30(degrees) with the table. Frictional resistance is equal to 5N. What is the acceleration of the mass? ans: 6.2 ms^-2

3) A coin can slife on a horizontal table. The coefficient of friction is 1/3. The coin is projected along the table with intial speed of 2ms^-1. Find the time before the coin comes to rest. ans: 0.6s


I'd appreciate any help.. thanks in advance!

[A.T]

1.As surface is smooth there would be no friction. Hence Fr=0N
First find horizontal component of force:-
F=20cos60=10N
As F=ma
a=F/m
a=10/4=2.5 ms-2

2.Fr=5N
D=Horizontal component of force(Driving force)
D=20cos30
Using D-Fr=ma
20cos30 - 5 =2a
a=6.16 ms-2

3. Fr=(U)N      (U)=Mew or whatever u call it (cofficient of friction)
N=mg
Fr=(U)N
ma=(U)mg
cancel m on both sides
a=(U)g
a=1/3 * 10
a= 10/3 ms-2

a is the deceleration produced, hence we will take it as '-'ve

a=(v-u)/t
-10/3 = (0-2)/t
t=0.6 sec


Feel free to ask any more question, or any thing u didnt understand from above. 

[7ooD]

thx A.t that waz great welcomez to the forum dude +rep for u 

[BurstBullet]

Thanks A.T! That was really helpful!

[A.T]

No Problem.

[BurstBullet]

More questions:

1) An empty bucket of mass 4kg is lowered from rest into a well by means of a light rope. The well is 50m in depth and the bucket is lowered with a constant acceleration of 6ms^-2. Calculate:
a. The tension in Newtons of the rope. ans: 26N
b. The time in seconds to 3 s.f. for the bucket to reach the bottom of the well. ans: 4.08s

2) A basket of mass 3kg is being pulled along a rough horizontal floor by a light rope inclined upward at an angle of 30(degrees) to the floor. The tension in the rope is 8N. Considering the basket as a particle. Calculate:

a. The magnitude of the normal component of the resultant force exerted on the basket by the floor. ans:26N
b. Given that the acceleration of the lanudry is 0.2ms^-2, find the coefficient of friction between the laundry basket and the floor. ans: 0.243

3) A  body of mass 4kg is pulled from rest to a speed of 4.5ms^-1 in time of 3 seconds on a rough horizontal surface by a force of 20N which makes an angle of 10(degrees- with the horizontal. Find the coefficient of friction. ans: 0.375

Thank in advance (:

[A.T]

1.a) Tension is in the upward direction.
Using:-
4g-T=ma
4(10)-T=4 *6
T=16N

b) s=ut + 1/2 *at^2
s=50
u=0
a=6
and by using these u will get t=4.08s

plz check your answer for 1a again.