physics help for exam please?????????

Question

a body of mass 0.51 Kg resting on a rough table(coefficient of friction=0.4) is conected by a light string over a smooth pully to a body of mass 0.42 Kg hanging freely.find the :
a)common accelertion of the two bodies

b) tension in the string
47 minutes ago - 3 days left to answer. - 1 answe

Answer 1

From Free body diagram:

Let m1=0.51 kg
m2=0.42 kg
T= tension

g=9.8 m/s^2
mu=0.4
N=0.51* g=4.998 N

T-mu*N=m1*a .....1
m2(g-a)- T =0.....2

we get m2(g-a) - mu*N = m1*a

(m1+ m2) * a = m2*g - mu*N
a= (9.8/0.93)*(0.42-0.4*0.51)
=2.276 m/s^2
T= 0.42(g-a) = 3.16N
Tension= m2*g=0.42*9.8=4.116 N

Answer 2

A free body diagram will help:

I Assume that acceleration due to gravity is 10 m/s^2 here.

5.1 N
F < O---------
~~~~~~~~O |
..........pulley |
...................|
..................O 4.2 N

The friction F is equal to: coefficient of friction x reaction of 0.51 kg mass
= 0.4 x 0.51 x 10
= 2.04

The net force accelerating in the direction of the string is hence
4.2 - 2.04
= 2.16 N

This 2.16 N force accelerates a net force of 0.93 (0.42 + 0.51).

Using F = ma,
acceleration, a = F/m
= 2.16 / 0.93
= 2.32 m/s^2

Tension in the string may be calculated by using any of the two masses:

With the 0.42 kg mass, resultant force, F = ma
= 0.42 * 2.32
= 0.98 N
Now the tension resists motion, therefore, resultant accelerating force = weight - tension

Tension = weight - resultant force
= (0.42*10) - 0.98
= 3.22 N

Answer 3

a) Force of friction is equal to: F = kW = (0.4)(0.51 kg)(9.81 m/s²) = 2.00 N

b) Force exerted by body connected over the smooth pully:

F2=(0.42)(9.81)= 4.12 N

c) Resulting force of tension in string:

Fd = F2 - F = 4.12-2 = 2.12 N

d) As there is a force that keeps body on the table moving, hence the resulting common acceleration is:

a= Fd / m = 2.12 N / (0.51+ 0.42)kg = 2.27 m/s²

Hope it helps!

Good luck!

Answer 4

F=ma
F is 4.2 -0.4= 3.8N, m is total mass in system 0.42+0.51=0.93
hence a (acceleration) =3.8/0.93= 4.086 m/s

0.51O-------->---------O0.42

T= (5.5-4.2)(4.086)=5.312N

Answer 5

A) for the answer of a is 0.95m/s(squared)

B)5.48N