Please help with circled section. Use the worked example above to help you solve

Question

Please help with circled section.

Use the worked example above to help you solve this problem. A block with mass m1- 4.50 kg and a ball with mass m2 = 7.50 kg are connected by a light string that passes over a frictionless pulley, as shown in figure (a). The coefficient of kinetic friction between the block and the surface is 0.300. (a) Find the acceleration of the two objects and the tension in the string. a = 5.0225 m/s2 T = 35.83 Check the answer for the acceleration by using the system approach. (Use the following as hecessary: mi, m2, Hk, and g.) EXERCISE HINTS: GETTING STARTED I I'M STUCK Use the values from PRACTICE IT to help you work this exercise. What if an additional mass is attached to the ball? How large must this mass be to increase the downward acceleration by 45%? kg Why isn't it possible to add enough mass to double the acceleration?

Explanation / Answer

First Question -

(b) Write the expression for mass m1 –

T – uk*m1g = m1*a

T = m1*a + uk*m1g----------------------------------------------(i)

The expression for mass m2 is –

m2g – T = m2*a

=> T = m2*g - m2a---------------------------------------(ii)

Equalize (i) and (ii) –

m1*a + uk*m1g = m2*g -m2a

=> a*(m1+ m2) = m2g – uk*m1g

=> a = (m2 – uk*m1)*g / (m1 + m2)

Second question –

First Part:

By attaching additional mass to the ball, the downward acceleration of the ball shall increase.

Second Part:

New acceleration, a = 5.0225 x 1.45 = 7.28 m/s^2

now put this value in the above expression –

7.28 = (m2 –0.30*4.50)*9.81 / (4.50 + m2)

=> 0.742*(4.50 + m2) = m2 – 1.35

=> 3.339 + m2*0.742 = m2 – 1.35

=> m2*0.258 = 4.689

=> m2 = 18.17 kg

Therefore, the mass shall be increased to 27.14 kg.

Third Part:

For doubling the acceleration –

new acceleration, a = 5.0225 x 2 = 10.045 m/s^2

put this value in the expression –

10.045 = (m2 –0.30*4.5)*9.81 / (4.5 + m2)

=> 1.02*(4.5 + m2) = m2 – 1.35

=> 4.59 + m2*1.02 = m2 – 1.35

=> m2*(1 – 1.02) = 5.94

=> m2 = - 297.0 kg

This value of mass m2 is negative, which is not possible.

Therefore, doubling the existing acceleration is not possible.

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