Two blocks with masses m1= 3.00 kg and m2=4.00 kg are connected by a light piece of red string. The red string is draped over a frictionless pulley. Block m, is positioned on a rough ramp that makes an angle of 37.0° with the horizontal, while block m2 is positioned on a rough horizontal tabletop to the left of the ramp. The coefficient of kinetic friction between mị and the ramp is µi= 0.250, and the coefficient of kinetic friction between m2 and the ramp is µ2= 0.100. Meanwhile, a third block of mass m3 = 0.0250 kg is connected to the other side of mass m2 with a piece of blue string. The blue string is draped over a second frictionless pulley so that mass m3 hangs vertically over the left side of the horizontal tabletop. When the system is released from rest, block m¡ travels down the ramp with an unknown acceleration a. Assume the strings connecting the blocks remain taut so that the whole system travels with the same acceleration. a=? a=? m2= 4.00 kg FTi=? a=? Fr2=? Hz = 0.100 m¡ = 3.00 kg µj = 0.250 m3= 0.0250 kg 0= 37.0° (a) Draw a complete free-body diagram for each individual mass (three diagrams total). Be sure to label each force as well as the positive x- and y-axes on each diagram. Do not split forces into components. (b) Calculate the following forces: (i) The normal force acting on mị (ii) The normal force acting on m2 (iii) The kinetic friction force acting on m¡ (iv) The kinetic friction force acting on m2 (c) Calculate the following quantities: (i) The acceleration of the three-block system (ii) The tension Fri in the red piece of string (iii) The tension Fr2 in the blue piece of string (d) Suppose m3 were replaced with a different mass M that enabled the system to travel at constant velocity. What would the value of M have to be?
Two blocks with masses m1= 3.00 kg and m2=4.00 kg are connected by a light piece of red string. The red string is draped over a frictionless pulley. Block m, is positioned on a rough ramp that makes an angle of 37.0° with the horizontal, while block m2 is positioned on a rough horizontal tabletop to the left of the ramp. The coefficient of kinetic friction between mị and the ramp is µi= 0.250, and the coefficient of kinetic friction between m2 and the ramp is µ2= 0.100. Meanwhile, a third block of mass m3 = 0.0250 kg is connected to the other side of mass m2 with a piece of blue string. The blue string is draped over a second frictionless pulley so that mass m3 hangs vertically over the left side of the horizontal tabletop. When the system is released from rest, block m¡ travels down the ramp with an unknown acceleration a. Assume the strings connecting the blocks remain taut so that the whole system travels with the same acceleration. a=? a=? m2= 4.00 kg FTi=? a=? Fr2=? Hz = 0.100 m¡ = 3.00 kg µj = 0.250 m3= 0.0250 kg 0= 37.0° (a) Draw a complete free-body diagram for each individual mass (three diagrams total). Be sure to label each force as well as the positive x- and y-axes on each diagram. Do not split forces into components. (b) Calculate the following forces: (i) The normal force acting on mị (ii) The normal force acting on m2 (iii) The kinetic friction force acting on m¡ (iv) The kinetic friction force acting on m2 (c) Calculate the following quantities: (i) The acceleration of the three-block system (ii) The tension Fri in the red piece of string (iii) The tension Fr2 in the blue piece of string (d) Suppose m3 were replaced with a different mass M that enabled the system to travel at constant velocity. What would the value of M have to be?
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Chapter1: Units, Trigonometry. And Vectors
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Please see the image attached. I only need part D. Thank you so much!
Transcribed Image Text:Problem 1
Two blocks with masses m1 = 3.00 kg and m2= 4.00 kg are connected by a light piece of red string. The red string is draped over a
frictionless pulley. Block m, is positioned on a rough ramp that makes an angle of 37.0° with the horizontal, while block m2 is
positioned on a rough horizontal tabletop to the left of the ramp. The coefficient of kinetic friction between mị and the ramp is µi=
0.250, and the coefficient of kinetic friction between m2 and the ramp is l2 = 0.100.
Meanwhile, a third block of mass m3 = 0.0250 kg is connected to the other side of mass m2 with a piece of blue string. The blue string
is draped over a second frictionless pulley so that mass m3 hangs vertically over the left side of the horizontal tabletop.
When the system is released from rest, block m, travels down the ramp with an unknown acceleration a. Assume the strings
connecting the blocks remain taut so that the whole system travels with the same acceleration.
a=?
a= ?
m2= 4.00 kg
Fri=?
a= ?
Fr2= ?
µz = 0.100
m1 = 3.00 kg
µj = 0.250
m3= 0.0250 kg
0= 37.0°
(a) Draw a complete free-body diagram for each individual mass (three diagrams total). Be sure to label each force as well as the
positive x- and y-axes on each diagram. Do not split forces into components.
(b) Calculate the following forces:
(i) The normal force acting on mị
(ii) The normal force acting on m2
(iii) The kinetic friction force acting on m,
(iv) The kinetic friction force acting on m2
(c) Calculate the following quantities:
(i) The acceleration of the three-block system
(ii) The tension Fri in the red piece of string
(iii) The tension Fr2 in the blue piece of string
(d) Suppose m3 were replaced with a different mass M that enabled the system to travel at constant velocity. What would the
value of M have to be?
1
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