A truncated cone is shown in the figure. The height of the truncated cone Time left...

  

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A truncated cone is shown in the figure. The height of the truncated cone Time left 0:39:22 smaller radius at the lower end is 0.3 m and the radius at the upper end is three times larger (0.9 m). The truncated cone is made of wood with a density p-500 kg/m³. The truncated cone can be considered to consist of a full cone of height. I minus a small cone of height H-A. Throughout the quesiton a subscript F refers to the full cone, and subscript Srefers to the small cone. a. Calculate the height of the full cone, H. m. H- (1 mark) b. Calculate the volume of the full cone, V (height H) and the and the volume of the smaller cone, Vs (height H-A). Vy= m³. m³. Vs (2 marks) c. Calculate the mass of the full cone, My, and the mass of the smaller cone, Ms. kg. kg. My Ms- d. Calculate the mass of the truncated cone, M. M- kg. (1 mark) e. The truncated cone is rotating about the z-axis. Determine the moment of inertia of the full cone about the z-axis, I, the moment of inertia of the small cone about the axis, Is and hence calculate the moment of inertia of the truncated cone about the axis, I Iram Is=" In- kg m² kg m² (2 mark) kg m² (3 marks) F. The truncated cone is subject to a torque applied about the z-axis given by T,- 400t Nm, where t is the time in seconds. By finding, and then integrating, an equation for the angular acceleration of the truncated cone, a, calculate the angular velocity of the truncated cone after 3 seconds. Wy rad/s. (3 marks) (3 marks) g. A point P, defined as (0.9/2, 0.9√2, 1.2], is on the upper rim of the truncated cone. Determine the velocity of this point after 3 seconds.. UPL-3= i+ j+ h. Calculate the acceleration of P at the same time. j+ GPt-3 H i+ h N Figure: Truncated cone km/s. km/s. y (3 marks) (5 marks) 2 A truncated cone is shown in the figure. The height of the truncated cone Time left 0:39:22 smaller radius at the lower end is 0.3 m and the radius at the upper end is three times larger (0.9 m). The truncated cone is made of wood with a density p-500 kg/m³. The truncated cone can be considered to consist of a full cone of height. I minus a small cone of height H-A. Throughout the quesiton a subscript F refers to the full cone, and subscript Srefers to the small cone. a. Calculate the height of the full cone, H. m. H- (1 mark) b. Calculate the volume of the full cone, V (height H) and the and the volume of the smaller cone, Vs (height H-A). Vy= m³. m³. Vs (2 marks) c. Calculate the mass of the full cone, My, and the mass of the smaller cone, Ms. kg. kg. My Ms- d. Calculate the mass of the truncated cone, M. M- kg. (1 mark) e. The truncated cone is rotating about the z-axis. Determine the moment of inertia of the full cone about the z-axis, I, the moment of inertia of the small cone about the axis, Is and hence calculate the moment of inertia of the truncated cone about the axis, I Iram Is=" In- kg m² kg m² (2 mark) kg m² (3 marks) F. The truncated cone is subject to a torque applied about the z-axis given by T,- 400t Nm, where t is the time in seconds. By finding, and then integrating, an equation for the angular acceleration of the truncated cone, a, calculate the angular velocity of the truncated cone after 3 seconds. Wy rad/s. (3 marks) (3 marks) g. A point P, defined as (0.9/2, 0.9√2, 1.2], is on the upper rim of the truncated cone. Determine the velocity of this point after 3 seconds.. UPL-3= i+ j+ h. Calculate the acceleration of P at the same time. j+ GPt-3 H i+ h N Figure: Truncated cone km/s. km/s. y (3 marks) (5 marks) 2