9. (7 points) A 5.00-kg mass with an initial velocity of 4.00 m/s, east collides

Question

9. (7 points) A 5.00-kg mass with an initial velocity of 4.00 m/s, east collides with a 4.00-kg mass with an initial velocity of 3.00 m/s, west. After the collision the 5.00-kg mass has a velocity of 1.20 m/s, south. a) What is the magnitude of the velocity of the 4.00-kg mass after the collision? b) In what direction is it moving? 10. (7 points) A mass m = 4.00 kg is connected, as shown, by a light cord to a mass M= 6.00 kg, which slides on a horizontal surface. The coefficient of kinetic friction between the mass M and the horizontal surface is -0.150. The pulley, which rotates about a frictionless axle and has a radius R = 0.120 m. may be treated as a uniform disk of mass mp 2.00 kg. The cord does not slip on the pulley a) What is the magnitude of the acceleration of m? b) What is the tension in the horizontal section of the cord?

Explanation / Answer

Let F be the tension in the hanging string

then

Torque due to F on pulley is T = R*F = I*alpha

alpha is the angular accelaration = a/R

I is the moment of inertia = 0.5*mp*R^2

then

R*F = (1/2)*mp*R^2*(a/R)^2

R*F = (1/2)*mp*a^2

and also using equation of motion to the m

mg-F = m*a

F = m(g-a)

then

R*m*(g-a) = (1/2)*mp*a^2

0.12*4*(9.8-a) = (1/2)*2*a^2

a = 1.95 m/s^2

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b) equation of motion to the M

M*a = F2-(mu_k*M*g)

F2 = M*a+(mu_k*M*g)

F2 = (6*1.95)+(0.15*6*9.81)

F2 = 20.53 N

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