#2.289 ms^-2# GIVEN #m_1=2 kg , m_2 =1kg# #"Coefficient of kinetic friction between " m_1 " and table" (mu_k)=0.15# # "Let"# #color (blue) T " be tension on string"# #" and " color(green) a" be the acceleration of the system "# Now considering the forces on #m_1# Normal reaction # N = m_1g# Resisting force of kinetic friction #f_k=mu_kxxN=mu_km_1g# Gravitational pull on #m_1# being vertical to T it will not creat any resistance. So for #m_1# we have #T-mu_km_1g=m_1a......(1)# Considering the forces on #m_2# we can write #m_2g-T=m_2a.....(2)# Adding equation (1) and equation(2) we get #m_2g-mu_km_1g=m_1a+m_2a# #=>a (m_1+m_2)=(m_2-mu_km_1)g# #=>a =((m_2-mu_km_1)g)/(m_1+m_2)=((1-0.15xx2)xx9.81)/(1+2)# #=(0.7xx9.81)/3=2.289ms^-2#

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In a pulley system, #m_1# is #2.0kg# and #m_2# is #1.0kg#. The coefficient of kinetic friction between #m_1# and the table is #mu_k=0.15#. What is the acceleration of the pulley system?

Answer 1

Leo Abeyta

#2.289 ms^-2#

GIVEN

#m_1=2 kg , m_2 =1kg#
#"Coefficient of kinetic friction between " m_1 " and table" (mu_k)=0.15#
# "Let"#
#color (blue) T " be tension on string"#
#" and " color(green) a" be the acceleration of the system "#
Now considering the forces on #m_1#
Normal reaction # N = m_1g#
Resisting force of kinetic friction #f_k=mu_kxxN=mu_km_1g#
Gravitational pull on #m_1# being vertical to T it will not creat any resistance.

So for #m_1# we have

#T-mu_km_1g=m_1a......(1)#
Considering the forces on #m_2# we can write

#m_2g-T=m_2a.....(2)#
Adding equation (1) and equation(2) we get

#m_2g-mu_km_1g=m_1a+m_2a#
#=>a (m_1+m_2)=(m_2-mu_km_1)g#
#=>a =((m_2-mu_km_1)g)/(m_1+m_2)=((1-0.15xx2)xx9.81)/(1+2)#
#=(0.7xx9.81)/3=2.289ms^-2#

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Answer 2

Benjamin Asiedu

The acceleration of the pulley system can be found using the equation: acceleration = (m2 - m1 * mu_k) / (m1 + m2), where m1 = 2.0 kg, m2 = 1.0 kg, and mu_k = 0.15. Plug in these values to find the acceleration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.