UNIT 4
PHYS 2001
Example 01
Example 02
Example 03
Example 04
Example 05
Example 06
Example 07

 

 

Static Equilibrium - Example 07

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A 50 kg wooden crate in Fig 7 rests on a wooden ramp with an adjustable angle of inclination and a coefficient of friction between the block and ramp of 0.30.
(a) Draw a free body diagram of the crate. 
(b) If the angle of the ramp is set to 10°, determine
(i) The component of the crate's weight that is perpendicular to the ramp 
(ii) The component of the crate's weight that is parallel to the ramp    
(iii) The normal force between the crate and the ramp
(iv) The static friction force between the crate and the ramp



Fig 7.
Answer  
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(a) F = Frictional force
R = Normal force
W = Weight of crate

 

 

Fig 2b.
 
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(b) Resolving W into parallel and perpendicular components to the plane

(i) Perpendicular Component = W Cos 10°
Perpendicular Component = 50 kg Cos 10°
Perpendicular Component = 40 kg

(ii) Parallel component = W Sin 10°
Parallel component = 50 kg Sin 10°
Parallel component = 8.7 kg

(iii) ∑F = 0 (Static Equilibrum)

∑Perpendicular forces = 0
W Cos 10° + R = 0
mg Cos 10° = - R
(50 kg X 9.81ms-2) Cos 10° = - R
R = - 483 N (minus sign indicates force is to the left)

(iv) ∑Parallel forces = 0
W Sin 10° + F = 0
mg Sin 10° = - F
-(50 kg X 9.81ms-2) Sin 10° = - F
F = 85.2 N



   
 

 

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Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.