A clerk moves a box of cans down an aisle by pulling on a strap attached to the box. The clerk pulls with a force of 188.0 N at an angle of 26 degrees with the horizontal. The box has a mass of 36 kg, and the coefficient of kinetic friction between the box and floor is 0.450. The acceleration due to gravity is 9.81 m/s^2. What is the acceleration of the box? Answer in units of m/s^2
Please show the steps
Please show the steps
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Basically you have 2 lateral forces acting on the box: the horizontal component of the force which the clerk is putting on the strap, and the friction force acting in the opposite direction (slowing the sliding of the box down).
Recall that the friction force is the normal force x the friction coefficient. The normal force (N) in this case will be the weight of the box minus the upward force which the strap is putting on the box. So:
N=W-188*sin(26)
N=mg-188*sin(26)
Friction force is then:
Ff=0.45*N
And the net force on the box is:
Fnet=188*cos(26) - Ff
Recall then from Newton's second law, Fnet=ma or a=Fnet/m
where m is the mass of the box
Fnet is the sum of all forces being put on the box
and the direction of positive acceleration is chosen to be the direction in which the clerk is pulling the box.
Easy peasy. Sub your values into the equations above, and follow them in order and you've got your answer.
Recall that the friction force is the normal force x the friction coefficient. The normal force (N) in this case will be the weight of the box minus the upward force which the strap is putting on the box. So:
N=W-188*sin(26)
N=mg-188*sin(26)
Friction force is then:
Ff=0.45*N
And the net force on the box is:
Fnet=188*cos(26) - Ff
Recall then from Newton's second law, Fnet=ma or a=Fnet/m
where m is the mass of the box
Fnet is the sum of all forces being put on the box
and the direction of positive acceleration is chosen to be the direction in which the clerk is pulling the box.
Easy peasy. Sub your values into the equations above, and follow them in order and you've got your answer.