4) Two blocks of mass m,= 3 kg and m,= 7 kg are connected by a massless string over a pulley with radius r = 0.25 m and mass M = 9 kg. There aren’t friction forces in inclined planes. The directions of acceleration a and angular acceleration a are given in Figure. (a) Draw free-body diagram. (b) Find the linear acceleration. (c) Find the angular acceleration.

Problem 9: Circular turns of radius r in a race track are often banked at an angle 0 to allow the cars to achieve higher speeds around the turns. Assume friction is not present, and use the coordinate system specified. F,

Determine the linear acceleration of a car that is traveling at 22 m/s around an 85 m radius curve.

3. Consider the Atwood's machine given below: m₁ m₂ Assume m₁ = 1.2 kg and m₂ = 1.5 kg. Neglect any rotational and frictional effect of the pulley. Assume the masses are released from rest. Find: (a) the acceleration a and the tension T experienced by m₁ and m₂ using Newton's 2nd Law of Motion; (b) the final velocities v₁ of m₁ and v₂ of m₂ when m₂ has descended 20 cm using Kinematics; (c) the final speeds v₁ of m₁ and v₂ of m2 when m₂ has descended 20 cm using the Work- Energy Theorem, and (d)) the final speeds v₁ of m₁ and v2 of m2 when m2 has descended 20 cm using the Conservation of Mechanical Energy. ANSWER ONLY A & B

A 2.40 kg mass attached to the end of a massless string swings in a vertical circle with radius 5.00 m at constant speed 6.75 m/s. At the instant when the string makes an angle of 35.0 degrees with the vertical, as shown in the figure, calculate the magnitude of the force (in N) that the string exerts on the mass. Round your answer to 1 decimal place.