1. The figure shows a box with mass m 1 on a frictionless plane inclined at angl

Question

1. The figure shows a box with mass m1 on a

frictionless plane inclined at angle ?1. The box is

connected via a cord of negligible mass to another

box with mass m2 on a frictionless plane inclined at

angle ?2 (> ?1). The pulley is frictionless and has

negligible mass and assumes that the setup is on the

surface of the earth.

a) Provide free-body force diagram for both boxes.

b) What is the acceleration in terms of m1, m2, ?1 and ?2?

c) What is the tension in the cord?

d) What situation can make the acceleration to be zero and what is the tension in the

cord then?

2. A loaded penguin sled weighing 100 N rests on a plane inclined at angle 30 to the

horizontal (see the figure). Between the sled and the plane, the coefficient of static

friction is 0.2, and the coefficient of kinetic friction is 0.1.

a) What is the least magnitude of the force F ,

parallel to the plane, which will prevent the

sled from slipping down the plane?

b) What is the minimum magnitude of the

force F that will start the sled moving up the

plane?

c) What value of F is required to move the

sled up the plane at constant velocity?

2. A loaded penguin sled weighing 100 N rests on a plane inclined at angle 30 to the horizontal (see the figure). Between the sled and the plane, the coefficient of static friction is 0.2, and the coefficient of kinetic friction is 0.1. a) What is the least magnitude of the force F , parallel to the plane, which will prevent the sled from slipping down the plane? b) What is the minimum magnitude of the force F that will start the sled moving up the plane? c) What value of F is required to move the sled up the plane at constant velocity? 1. The figure shows a box with mass m1 on a frictionless plane inclined at angle ?1. The box is connected via a cord of negligible mass to another box with mass m2 on a frictionless plane inclined at angle ?2 ( > ?1). The pulley is frictionless and has negligible mass and assumes that the setup is on the surface of the earth. a) Provide free-body force diagram for both boxes. b) What is the acceleration in terms of m1, m2, ?1 and ?2? c) What is the tension in the cord? d) What situation can make the acceleration to be zero and what is the tension in the cord then?

Explanation / Answer

1. The largest force is related to the max acceleration
consider m2 at the point the cord is on the verge of slack
m2*g*sin(?)=m2*a
a=g*sin(?)

Therefore
Fmax=m1*g*sin(?)

2.

a) A FBD of the sled at rest yields force parallel to the incline as
F+100*cos(30)*0.2-100*sin(30)=0
F=32.68 N

b)
F-100*cos(30)*.2-100*sin(20)=0
F=67.32 N

c)
F-100*cos(30)*.1-100*sin(30)=0
F=58.66 N

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