QuestionR1. A hydraulic press is used to compact powdered samples. The device is made of two interconnected cylindrical chambers filled with oil of density po and closed by two pistons. The small chamber on the right has diameter d and the large chamber on the left has diameter 5d. A lever is attached to the piston pushing down on the fluid in the small cylinder. The horizontal lever is hinged on the left, at distance L from the small piston, and a force of magnitude Fo is applied vertically down at distance 2L from the hinge (see figure). You may assume that the lever and pistons have negligible mass. powdered sample large static frame piston Fo hinge lever 5d L oil small piston Figure 1: Setup for question 1 (a) Determine the magnitude of the force Fin that the small piston exerts 1 on the fluid in the small cylinder. Hint: you may consider that the lever is at rest in the horizontal position. (b) Determine the pressure change applied to the fluid by the small piston. (c) Determine the magnitude Fout of the force that the fluid applies to the large piston.

International Edition---engineering Mechanics: Statics, 4th Edition
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ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
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Chapter8: Centroids And Distributed Loads
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QuestionR1.
A hydraulic press is used to compact powdered samples. The device is made
of two interconnected cylindrical chambers filled with oil of density po and
closed by two pistons. The small chamber on the right has diameter d and
the large chamber on the left has diameter 5d. A lever is attached to the
piston pushing down on the fluid in the small cylinder. The horizontal lever
is hinged on the left, at distance L from the small piston, and a force of
magnitude Fo is applied vertically down at distance 2L from the hinge (see
figure). You may assume that the lever and pistons have negligible mass.
powdered
sample large
static
piston
frame
Fo
hinge
lever
5d
L
oil
small
piston
Figure 1: Setup for question 1
(a) Determine the magnitude of the force Fin that the small piston exerts
1
on the fluid in the small cylinder. Hint: you may consider that the
lever is at rest in the horizontal position.
(b) Determine the pressure change applied to the fluid by the small piston.
(c) Determine the magnitude Fout of the force that the fluid applies to the
large piston.
(d) A fragment of the metallic frame of density Pm (Pm > p.) and volume
V accidentally fell into the oil chamber and is sitting at the bottom.
Determine the magnitude of the normal force exerted on the fragment
of metal by the bottom of the oil chamber.
Transcribed Image Text:QuestionR1. A hydraulic press is used to compact powdered samples. The device is made of two interconnected cylindrical chambers filled with oil of density po and closed by two pistons. The small chamber on the right has diameter d and the large chamber on the left has diameter 5d. A lever is attached to the piston pushing down on the fluid in the small cylinder. The horizontal lever is hinged on the left, at distance L from the small piston, and a force of magnitude Fo is applied vertically down at distance 2L from the hinge (see figure). You may assume that the lever and pistons have negligible mass. powdered sample large static piston frame Fo hinge lever 5d L oil small piston Figure 1: Setup for question 1 (a) Determine the magnitude of the force Fin that the small piston exerts 1 on the fluid in the small cylinder. Hint: you may consider that the lever is at rest in the horizontal position. (b) Determine the pressure change applied to the fluid by the small piston. (c) Determine the magnitude Fout of the force that the fluid applies to the large piston. (d) A fragment of the metallic frame of density Pm (Pm > p.) and volume V accidentally fell into the oil chamber and is sitting at the bottom. Determine the magnitude of the normal force exerted on the fragment of metal by the bottom of the oil chamber.
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