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This last problem set my professor gave has left me befuddled. I feel like I am missing some intuition to solve these problems. The book isn't helping much, as I have spent hours in it. I have a few problems that I need some kind of head start on.
You are designing a conveyor system for a gravel yard. A hopper drops gravel at a rate of 77.5 kg/s onto a conveyor belt that moves at a constant speed v = 2.20 m/s. Suppose the conveyor belt is retarded by a friction force of 150 N. Determine the required output power (hp) of the motor as a function of time from the moment gravel first starts falling (t=0) until 4 s after the gravel begins to be dumped off the end of the 25 m long conveyor belt.
Ma=F_ext + v_rel(dM/dt) seems to be usedd here
a=0, so P=Fv=(v)(v)(dM/dt)=(2.2)(2.2)(77.5) which is wrong but I don't know how to start in the right direction from here. I am also confused how you can incorporate the 4 seconds after some gravel has left the belt into that equation.
The jet engine of an airplane takes in 130 kg of air per second, which is burned with 4.3 kg of fuel per second. The burned gases leave the plane at a speed of 600 m/s (relative to the plane). If the plane is traveling 260 m/s , determine the power (hp) delivered.
Ma=F_ext + v_rel(dM/dt)
W=Fv
I tried (velocity of ejected fuel)(rate of fuel plus rate of air going out of system)(velocity of ejected fuel) which did not work either and I am again stumped.
An Atwood's machine consists of two masses, m_A and m_B, which are connected by a massless inelastic cord that passes over a pulley.If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses m_A and m_B. [Hint: The tensions are not equal.]
I used F=ma for each of the masses and Torque=I(angular acceleration)
I had the two torques from the masses equal to I(angular acceleration). But my linear accelerations ended up canceling out and that's what I am solving for! So i have a feeling there is a third torque at work here. I am befuddled.
Homework Statement
You are designing a conveyor system for a gravel yard. A hopper drops gravel at a rate of 77.5 kg/s onto a conveyor belt that moves at a constant speed v = 2.20 m/s. Suppose the conveyor belt is retarded by a friction force of 150 N. Determine the required output power (hp) of the motor as a function of time from the moment gravel first starts falling (t=0) until 4 s after the gravel begins to be dumped off the end of the 25 m long conveyor belt.
Homework Equations
Ma=F_ext + v_rel(dM/dt) seems to be usedd here
The Attempt at a Solution
a=0, so P=Fv=(v)(v)(dM/dt)=(2.2)(2.2)(77.5) which is wrong but I don't know how to start in the right direction from here. I am also confused how you can incorporate the 4 seconds after some gravel has left the belt into that equation.
Homework Statement
The jet engine of an airplane takes in 130 kg of air per second, which is burned with 4.3 kg of fuel per second. The burned gases leave the plane at a speed of 600 m/s (relative to the plane). If the plane is traveling 260 m/s , determine the power (hp) delivered.
Homework Equations
Ma=F_ext + v_rel(dM/dt)
W=Fv
The Attempt at a Solution
I tried (velocity of ejected fuel)(rate of fuel plus rate of air going out of system)(velocity of ejected fuel) which did not work either and I am again stumped.
Homework Statement
An Atwood's machine consists of two masses, m_A and m_B, which are connected by a massless inelastic cord that passes over a pulley.If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses m_A and m_B. [Hint: The tensions are not equal.]
Homework Equations
I used F=ma for each of the masses and Torque=I(angular acceleration)
The Attempt at a Solution
I had the two torques from the masses equal to I(angular acceleration). But my linear accelerations ended up canceling out and that's what I am solving for! So i have a feeling there is a third torque at work here. I am befuddled.
