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A box in ‘no gravity' condition (outer space) is driven by a constant force (F) and...
1. (a) Figur1 shows the forces acting on a particle that falls from rest under gravity and is subject to a retarding force proportional to its velocity, bv Figure 1 mg (0) Show that the velocity, v,...
1. (a) Figur1 shows the forces acting on a particle that falls from rest under gravity and is subject to a retarding force proportional to its velocity, bv Figure 1 mg (0) Show that the velocity, v, as a function of time,t,can be written as 1-e m 151 (i) Determine an expression for the particle's terminal velocity. 2] 151 Find the position as a function of time. (b) The terminal velocity of the particle is 50 ms1. Find (c) (i)...
The voice coil shown below is driven with an input voltage Vin. We are interested in the motion o...
The voice coil shown below is driven with an input voltage Vin. We are interested in the motion of the load m, which moves with velocity v-x. 000o 00O0 Voice Coil Consider the voice coil to be ideal, with lumped resistance R. Neglect the voice coil inductance, voice coil inertia, and any translational damping. The voice coil equations are: where the direction of the applied force F on the mass is the same as x. Find the differential equation for...
Problem 1 Consider a paper airplane that has a rubber band driven propeller. The equations of...
Problem 1 Consider a paper airplane that has a rubber band driven propeller. The equations of motion for it longitu dinal dynamics can be written as where its state vector is given by the velocity V and the flight path angle y, i.e., xV,E R2, and the control input is given by the thrust u. All of other variables, namely mass m, gravitational acceleration g, lift parameters I, and drag parameter d are fixed constants (a) Let V* > 0...
A space probe is traveling in outer space with a momentum that has a magnitude of...
A space probe is traveling in outer space with a momentum that has a magnitude of 4.96 x 10 kg.m/s. A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of 1.93 x 10 N and a direction opposite to the probe's motion. It fires for a period of 10.7 s. Determine the momentum of the probe after the retrorocket ceases to fire. A 48.0-kg skater is standing at rest...
1. If a sky-diver jumps out of a plane, two forces will act on him, gravity...
1. If a sky-diver jumps out of a plane, two forces will act on him, gravity and air resistance. If we assume air resistance is proportional to the velocity, we get the total force on the sky diver will be F = −gm − kv, where g is a acceleration due to gravity on the surface of the earth, m is the mass of the sky-diver, v is the velocity of the sky-diver, and k is constant of proportionality for...
A 1.00 kg glider attached to a spring with a force constant 25.0 N/m oscillates on...
A 1.00 kg glider attached to a spring with a force constant 25.0 N/m oscillates on a horizontal, frictionless air track. At t = 0, the glider is released from rest at x = -2.70 cm. (That is, the spring is compressed by 2.70 cm.) (a) Find the period of its motion. s (b) Find the maximum values of its speed and acceleration. m/s m/s2 (c) Find the position, velocity, and acceleration as functions of time (t). x(t) = cm...
A 1.00-kg glider attached to a spring with a force constant 16.0 N/m oscillates on a...
A 1.00-kg glider attached to a spring with a force constant 16.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -2.50 cm (that is, the spring is compressed by 2.50 cm). (a) Find the period of the glider's motion. s (b) Find the maximum values of its speed and acceleration. speed m/s acceleration m/s2 (c) Find the position, velocity, and acceleration as functions of time. (Where position...
3. A 180-Ib person jumps out of an airplane with initial upward velocity of 5 ft/s...
3. A 180-Ib person jumps out of an airplane with initial upward velocity of 5 ft/s at a height of 3000 ft (assuming the air resistance is proportional to its falling speed). The air resists the body's motion with a force of 2 lb for each ft/s of speed. Assuming the constant gravity is 32 ft/s2. 1. find its velocity v = v(t) 2. find its terminal velocity 3. find the distance of falling x = x(t) 4. find the...
An object of mass m is connected to a light spring with a force constant of...
An object of mass m is connected to a light spring with a force constant of kH N/meter which oscillates on a frictionless horizontal surface with Simple Harmonic Motion. At t = 0 the spring was at rest but is compressed x = A meter maximum during oscillation. Write the equation of motion from Newton's 2nd law FH = m·a and Hook's Law FH = -kH·x. Because of the starting position assume a solution is x = A sin(ωt) a...
2. An object of 5 kg is released from rest 1000 meters above the ground level...
2. An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under the influence of gravity. Assuming that the force due to air resistance is proportional to the velocity of the object with proportionality constant k = 50 kg/sec determine the formula for the velocity of the object 3. A rocket having an initial mass mo kg is launched vertically from the surface of the Earth. The rocket expels gas at...
1. (a) Figur1 shows the forces acting on a particle that falls from rest under gravity and is subject to a retarding force proportional to its velocity, bv Figure 1 mg (0) Show that the velocity, v, as a function of time,t,can be written as 1-e m 151 (i) Determine an expression for the particle's terminal velocity. 2] 151 Find the position as a function of time. (b) The terminal velocity of the particle is 50 ms1. Find (c) (i)...
The voice coil shown below is driven with an input voltage Vin. We are interested in the motion of the load m, which moves with velocity v-x. 000o 00O0 Voice Coil Consider the voice coil to be ideal, with lumped resistance R. Neglect the voice coil inductance, voice coil inertia, and any translational damping. The voice coil equations are: where the direction of the applied force F on the mass is the same as x. Find the differential equation for...
Problem 1 Consider a paper airplane that has a rubber band driven propeller. The equations of motion for it longitu dinal dynamics can be written as where its state vector is given by the velocity V and the flight path angle y, i.e., xV,E R2, and the control input is given by the thrust u. All of other variables, namely mass m, gravitational acceleration g, lift parameters I, and drag parameter d are fixed constants (a) Let V* > 0...
A space probe is traveling in outer space with a momentum that has a magnitude of 4.96 x 10 kg.m/s. A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of 1.93 x 10 N and a direction opposite to the probe's motion. It fires for a period of 10.7 s. Determine the momentum of the probe after the retrorocket ceases to fire. A 48.0-kg skater is standing at rest...
3. A 180-Ib person jumps out of an airplane with initial upward velocity of 5 ft/s at a height of 3000 ft (assuming the air resistance is proportional to its falling speed). The air resists the body's motion with a force of 2 lb for each ft/s of speed. Assuming the constant gravity is 32 ft/s2. 1. find its velocity v = v(t) 2. find its terminal velocity 3. find the distance of falling x = x(t) 4. find the...
2. An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under the influence of gravity. Assuming that the force due to air resistance is proportional to the velocity of the object with proportionality constant k = 50 kg/sec determine the formula for the velocity of the object 3. A rocket having an initial mass mo kg is launched vertically from the surface of the Earth. The rocket expels gas at...
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