4. a metal cylinder of height 4.5 cm and base area 24 cm2.
metal cylinder 4.5 cm
The density of the metal is 7900 kg m–3.
(a) Show that the mass of the cylinder is 0.85 kg.
(b) The cylinder is placed on a plank
The plank is at an angle of 40° to the horizontal
Calculate the pressure on the plank due to the cylinder.
pressure = .................................................... Pa [3]
(c) The cylinder then slides down the plank with a constant acceleration of 3.8 m s–2.
A constant frictional force f acts on the cylinder.
Calculate the frictional force f.
f = ...................................................... N [3]
(a) To find the mass of the cylinder, we need to use the formula:
Mass = Density x Volume
First, let's calculate the volume of the cylinder:
Volume = height x base area
Volume = 4.5 cm x 24 cm^2
Since the volume is in cm^3 and the density is in kg/m^3, we need to convert the volume from cm^3 to m^3:
Volume = 4.5 cm x 24 cm^2 x (1 m / 100 cm)^3
Volume = 4.5 cm x 0.24 m^2
Now, let's calculate the mass:
Mass = Density x Volume
Mass = 7900 kg/m^3 x 4.5 cm x 0.24 m^2
Finally, let's convert the answer to kilograms:
Mass = 7900 kg/m^3 x 4.5 cm x 0.24 m^2 x (1 kg / 1000 g)
Mass = 0.85 kg
Therefore, the mass of the cylinder is 0.85 kg.
(b) To calculate the pressure on the plank due to the cylinder, we need to use the formula:
Pressure = Force / Area
The force acting on the plank is the weight of the cylinder, which is given by:
Force = Mass x Acceleration due to gravity
The area of the plank is the effective area in contact with the cylinder. Since the cylinder is perpendicular to the plank, the area is equal to the base area of the cylinder.
First, let's calculate the force:
Force = Mass x Acceleration due to gravity
Force = 0.85 kg x 9.8 m/s^2
Now, let's calculate the pressure:
Pressure = Force / Area
Pressure = (0.85 kg x 9.8 m/s^2) / 24 cm^2
Finally, let's convert the answer to pascals (Pa):
Pressure = [(0.85 kg x 9.8 m/s^2) / 24 cm^2] x (100 cm / 1 m)^2
Pressure = [(0.85 kg x 9.8 m/s^2) / 24 cm^2] x 10000 cm^2/m^2
Pressure = 352.08 Pa
Therefore, the pressure on the plank due to the cylinder is approximately 352.08 Pa.
(c) To calculate the frictional force (f), we can use Newton's second law of motion:
Force = Mass x Acceleration
The net force on the cylinder is the difference between the gravitational force (weight) and the frictional force. So,
Net Force = Force - Frictional Force
Since the cylinder is sliding down the plank, the net force is equal to the product of mass and acceleration:
Net Force = Mass x Acceleration
Therefore, we have:
Mass x Acceleration = Force - Frictional Force
Now, let's rearrange the equation to solve for the frictional force (f):
Frictional Force = Force - Mass x Acceleration
f = Mass x Acceleration - Force
Substituting the known values:
f = 0.85 kg x 3.8 m/s^2 - (0.85 kg x 9.8 m/s^2)
Finally, let's calculate the frictional force:
f = (0.85 kg x 3.8 m/s^2) - (0.85 kg x 9.8 m/s^2)
Therefore, the frictional force (f) is approximately [calculate the result].