7. A box with cargo of known total mass m₁ can be moved up or down by a rope running around a pulley. The other end of the rope is attached to a block of mass m₂. The block of mass m₂ acts as a counterweight and that can slide on a ramp of known angle 0, as shown. The rope is massless, unstretchable, and slides without friction on the pulley. The pulley can be assumed to be massless and only changes the direction of the rope. m 1 m₂ a. If the counterweight can slide without friction on the ramp, how does m₂ have to be chosen so that the cargo moves up or down with constant speed? b. If the coefficient of friction between the ramp and the counterweight is known to be fly how does my have to be chosen so that the cargo is lifted a height h from rest in a given time t₁? c. In the situation of (b), what is the tension in the rope?
7. A box with cargo of known total mass m₁ can be moved up or down by a rope running around a pulley. The other end of the rope is attached to a block of mass m₂. The block of mass m₂ acts as a counterweight and that can slide on a ramp of known angle 0, as shown. The rope is massless, unstretchable, and slides without friction on the pulley. The pulley can be assumed to be massless and only changes the direction of the rope. m 1 m₂ a. If the counterweight can slide without friction on the ramp, how does m₂ have to be chosen so that the cargo moves up or down with constant speed? b. If the coefficient of friction between the ramp and the counterweight is known to be fly how does my have to be chosen so that the cargo is lifted a height h from rest in a given time t₁? c. In the situation of (b), what is the tension in the rope?
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Transcribed Image Text:7. A box with cargo of known total mass m₁ can be moved up or down by a rope running
around a pulley. The other end of the rope is attached to a block of mass m₂. The block
of mass m₂ acts as a counterweight and that can slide on a ramp of known angle 0, as
shown. The rope is massless, unstretchable, and slides without friction on the pulley. The
pulley can be assumed to be massless and only changes the direction of the rope.
m1
M2
Ө
a. If the counterweight can slide without friction on the ramp, how does m₂ have to be
chosen so that the cargo moves up or down with constant speed?
b. If the coefficient of friction between the ramp and the counterweight is known to be µ,
how does m₂ have to be chosen so that the cargo is lifted a height h from rest in a given
time t₁?
c. In the situation of (b), what is the tension in the rope?
Expert Solution
Step 1: Know the concept:
Newton's second law:
According to Newton's second law, the net force on an object is equal to the product of its mass and net acceleration.
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