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5 parts
i

100 N\text{100 N}

ii

50 N\text{50 N}

v

4 m/s2\text{4 m/s}^2

iii

90 N\text{90 N}

iv

100 N\text{100 N}

Step-by-step solution

5 steps

Here are the calculations for each part of the problem:

Given:
Mass of body P, mP=10 kgm_P = 10 \text{ kg}
Mass of body Q, mQ=15 kgm_Q = 15 \text{ kg}
Coefficient of friction, μ=0.5\mu = 0.5
Acceleration due to gravity, g=10 m/s2g = 10 \text{ m/s}^2

Part i· 1 step

Normal reaction on P

  1. Calculate the normal reaction force on body P.

    The normal reaction force NN on body P is equal to its weight, as it rests on a horizontal surface.

    N=mPgN = m_P g

    Substitute the given values:

    N=(10)(10)N = (10)(10) N=100 NN = \boxed{\text{100 N}}

Part ii

50 N\text{50 N}

Frictional force between P and the surface

  1. Calculate the frictional force.

    The frictional force FfF_f is given by the product of the coefficient of friction and the normal reaction force.

    Ff=μNF_f = \mu N

    Substitute the values:

    Ff=(0.5)(100)F_f = (0.5)(100) Ff=50 NF_f = \boxed{\text{50 N}}

Part v

4 m/s2\text{4 m/s}^2

Common acceleration of P and Q

  1. Calculate the common acceleration of the system.

    The net force causing acceleration is the weight of Q minus the frictional force on P. The total mass of the system is mP+mQm_P + m_Q.

    a=mQg−FfmP+mQa = \frac{m_Q g - F_f}{m_P + m_Q}

    Substitute the values:

    a=(15)(10)−5010+15a = \frac{(15)(10) - 50}{10 + 15} a=150−5025a = \frac{150 - 50}{25} a=10025a = \frac{100}{25} a=4 m/s2a = \boxed{\text{4 m/s}^2}

Part iii

90 N\text{90 N}

Tension in the string

  1. Calculate the tension in the string.

    Consider the forces acting on body Q. The weight of Q acts downwards, and the tension acts upwards. The net force causes Q to accelerate downwards.

    mQg−T=mQam_Q g - T = m_Q a

    Rearrange the equation to solve for TT:

    T=mQg−mQaT = m_Q g - m_Q a T=mQ(g−a)T = m_Q (g - a)

    Substitute the values:

    T=(15)(10−4)T = (15)(10 - 4) T=(15)(6)T = (15)(6) T=90 NT = \boxed{\text{90 N}}

Part iv

100 N\text{100 N}

Force which causes P and Q to accelerate

  1. Calculate the net force causing acceleration.

    This is the net force on the entire system, which is the product of the total mass and the common acceleration.

    Fnet=(mP+mQ)aF_{\text{net}} = (m_P + m_Q) a

    Substitute the values:

    Fnet=(10+15)(4)F_{\text{net}} = (10 + 15)(4) Fnet=(25)(4)F_{\text{net}} = (25)(4) Fnet=100 NF_{\text{net}} = \boxed{\text{100 N}}
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