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Question 1.
The 75-kg man climbs up the rope with an acceleration of 0.25 m/s2, measured relative to the rope. Determine the tension in the rope and the acceleration of the 80-kg block.

Question 2.
Calculate the vertical acceleration a of the 150 kg cylinder for each of the two cases illustrated. Neglect friction and the mass of the pulleys. Explain why the accelerations are different.

Question 3.
The steel ball is suspended from the accelerating frame by the two cords A and B. Determine the acceleration a of the frame which will cause the tension in cord A to be twice that in cord B.

Question 4.
A block of 2 kg mass is hanging from a spring with stiffness k = 70 N/m. The spring has an unstretched length of 30 cm. The mass oscillates vertically under the influence of the spring and gravity. Calculate the magnitude and direction of the mass’s acceleration when a) x = 40cm, b) x=75cm.

Question 5.
A block of 1 kg mass is hanging from a spring with stiffness k = 30 N/m. The spring has an unstretched length of 20 cm. The mass oscillates vertically under the influence of the spring and gravity. Calculate the two values of x for which the magnitude of the block’s acceleration is 6 m/s2.

Question 6.
The 0.8 kg collar slides with negligible friction on the fixed rod in the vertical plane. The collar starts from rest at point A and moves under the action of a constant, horizontal 8 N force, and gravity. Calculate the collar’s velocity as it hits stop at B.

Question 7.
The small body has a speed vA = 5 m/s at point A. Neglecting friction, determine its speed at point B after it has risen 0.8 m. Is knowledge of the shape of the track necessary to answer this question

Question 8.
An 80 kg pole vaulter carrying a uniform 4.9 m, 4.5 kg pole approaches the jump with velocity v and manages to barely clear the bar set at a height of 5.5 m. As he clears the bar, his velocity and that of the pole are essentially zero. Calculate the minimum possible value of v required for him to make the jump. Both the horizontal pole and the centre of gravity of the vaulter are 1.1 m above the ground during the approach.

Question 9.
The motor unit shown raises the 300 kg mass at 2 m/s. What is the power that the electric motor must provide