5. A solid sphere of radius 0.3 m and mass 5 kg rolls down the incline without slipping as shown in the figure below. Determine the acceleration and angular acceleration of the sphere. Use 0 = 30°. R

8. 2) Rods AB and BC are linked at Band have weights of 18 lb and 37 lb, respectively. The 8-lb collar C, which is connected to BC and the spring, slides freely along the smooth vertical guide. The lengths of the rods are 4 = 1.4 ft and 2 = 2.9 ft. If the system is released from rest when 0 = 0°, determine the magnitude of the angular velocity (in rad/s) of rod BC when 0 = 90°. The attached spring has spring constant k = 20 Ib/ft, and is unstretched when 0 = 0°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g= 32.2 ft/s2. k CO Your Answer: Answer

Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A force P of magnitude 4.4 N is applied to a tape wrapped around the body indicated. The body rests on a frictionless horizontal surface. Assume the mass of the uniform disk to be 2.4 kg. Determine the acceleration of Point A. B P The acceleration of Point A is 7.967 m/s m/s² →.

4. A pair of connected pulleys receive a force F = 75 N and P = 150 N as depicted in the image. The pulley system has a radius of gyration of ko 0.5 m and mass of 50kg. The radius of pulley 1 is r₁ = 600 mm, and the radius of pulley 2 is r2 = 1000 mm. Determine the angular velocity of the pulley system after it undergoes 2 revolutions starting from rest. F P₁ P

The spool has a mass of 105 kg and a radius of gyration of kg = 200 mm about its center of mass G. Assume the spool rolls without slipping. If a vertical force of P = 215 N is applied to the cable, determine the acceleration of G. (Figure 1) Express your answer with the appropriate units. HẢ ? Value m/s aG = Determine the angular acceleration of the spool. Express your answer with the appropriate units. HA Value rad /s? 300 mm a = G 150 mm

Solving dynamics problems in steps: 1. Collect data and assumptions 2. Desired result? 3. Make drawing/sketch of the (sub)problem 4. Equations and calculations 5. Answer and conclusions Furthermore: - - - Write down the steps clearly Check intermediate results (accuracy) Dimension check and units! Magnitude of number in line with expectation?

The mass of gear A is 25 kg and its centroidal radius of gyration is 105 mm. The mass of gear B is 13 kg and its centroidal radius of gyration is 85 mm. Calculate the angular acceleration of gear B when a torque of 16 N-m is applied to the shaft of gear A. Neglect friction. The angular acceleration is positive if counterclockwise, negative if clockwise. TA = 165 mm TB = 125 mm

The device shown is a simplified model of an amusement-park ride in which passengers are rotated about the vertical axis of the central post at an angular speed Q while sitting in a pod which is capable of rotating the occupants 360° about the longitudinal axis of the connecting arm attached to the central collar. Determine the percent increase n in angular velocity between configurations (a) and (b), where the passenger pod has rotated 90° about the connecting arm. For the model, m = 1.1 kg, r = 70 mm, I = 315 mm, and L = 640 mm. The post and connecting arms rotate freely about the z-axis at an initial angular speed 2 = 125 rev/min and have a combined mass moment of inertia about the z-axis of 38(10-3) kg m?. %3D (b) Ω (a) -Frame Pod Answer: n = %

Subject: civil engineering

The 150-kg wheel shown in Fig. In the initial position shown, the velocity of Gis 2 m/s down the plane, and the spring is stretched 150 mm. If the spring modulus is 1000 N/m, what will be the maximum stretch of the spring? has a radius of gyration of 360 mm with respect to its center of mass G. www 150 kg 30°