Please show every step. Thank you in advance. 1. Two people (a child and parent)

Question

Please show every step. Thank you in advance.

1. Two people (a child and parent) are sitting on a teeter-totter of length L = 3 m and mass m = 10 kg. There is a single support in the middle. The adult has a mass of m1 = 75 kg and the child has a mass of m2 = 30 kg. (a) Draw a free body diagram for the system consisting of the people and teeter-totter. (b) If the child sits on the end of the teeter-totter, where must the adult sit to balance it? 2. A 60 kg person is about to walk a uniform plank. The 45 kg plank rests on two pivots as shown. (a) The person is between the pivots a distance D from the left end. Determine the normal force exerted by each pivot. Use D = 1.5 m, S = 3.75 m and L = 6 m. (b) The person is now on the far right. How far can he walk past the second pivot (H) before the whole thing tips? 3. A uniform ladder of length L and mass m1 rests against a frictionless wall. The ladder makes an angle theta with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when a firefighter of mass m is a distance x from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is a distance s from the bottom, what is the coefficient of static friction between the ladder and ground?

Explanation / Answer

1) m2*(l/2) = m1*x1

x1 = 0.6 from the middle of the teeter totter

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2)

parta)

net torque about the left end =0

M1*g*D + m*g*(L/2) = Fr*s

(60*9.8*1.5)+(45*9.8*3) = Fr*3.75

Fr = 588 N

net force along vertical is zerro

Fl + Fr - M1*g - m*g = 0

Fl = 441 N

part b)

net torque about the right pivot = 0

M1*g*H + m*g*(L/2) - (L-s)) = Fl*s

(60*9.8*H) + (45*9.8*0.75) = 441*3.75

H = 2.25 m

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#3) ladder

along vertical

Fy net = 0

N1 - w_L - W_p = 0

N1 = (m1+m2)*g

force exerted by ground = N1

frictional force f = u*N1

alog horizantal

fx - N2 = 0

fx = N2

net torque = 0

W_l*(L/2)*cos? + W_p*s*cos? = N2*L*sin?

(m1*g*L/2*cos? ) + (m2*g*s*cos? ) = N2*L*sin?

0.5*m1*g*L*cos? + m2*g*s*cos? = u*(m1+m2)*g*L*sin?

u = g*cos? *(m2*s + 0.5*m1*L) / (m1+m2)*L*sin ?

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