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Q3:- Body will be free vibrate from rest and distance Im under action of force ft)...
Q3:- Body will be free vibrate from rest and distance Im under action of force f(t)...
Q3:- Body will be free vibrate from rest and distance Im under action of force f(t) = 3 sint by used second order differential equation find the equation of motion and find distance at t - 1 sec. Given (m= 1 kg & k= 4 N.m). Solution:-
If a body of mass m falling from rest under the action of gravity encounters an...
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
Q3) A mass of 3 kg moves horizontally along x axis under the action of a force depends on time , given as following...
Q3) A mass of 3 kg moves horizontally along x axis under the action of a force depends on time , given as following: F(t)4N where t in seconds, a) Find the impulse of this force during the interval t= 0 to t-2 S, if the mass starts motion from rest at x-0 b) Find its velocity and position as function of time.
A 50kg skydiver jumps out of an airplane. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude cv^2 where c=.1275 kg/m and i
A 50kg skydiver jumps out of an airplane. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude cv^2 where c=.1275 kg/m and is the velocity of the skydiver at time t (and upward is positive velocity). The gravitational constant is 9.8 m/s^2 . a) Find a differential equation for the velocity. b) Determine the terminal velocity in...
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...
GROUP PROBLEM-1 SAN FRANCISCO STATE UNIVERSITY Given: The 300-kg bar B, originally at rest, is towed...
GROUP PROBLEM-1 SAN FRANCISCO STATE UNIVERSITY Given: The 300-kg bar B, originally at rest, is towed over a series of small rollers. The motor M is drawing in the cable at a rate of v (0.4 t2) m/s, where t is in seconds. Find: Force in the ca ble and distance s whent 5s. Plan: Since both forces and velocity are involved, this problem requires both kinematics and the equation of motion. 1) Draw the free-body and kinetic diagrams of...
The wheel shown in the diagram starts from rest under the application of the constant force...
The wheel shown in the diagram starts from rest under the
application of the constant force P=10 N. The wheel has a mass of
m=3 kg and a radius of gyration about its center of mass of and
kinetic coefficients of friction between the wheel and the inclined
plane are At the instant shown, the center of the wheel, G, has a
speed of 2 m/s. . The static and . (4 marks) (5 marks) (7 marks) (4
marks) a)...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
An object of mass 700 kg is released from rest 1000 m above the ground and...
An object of mass 700 kg is released from rest 1000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b=50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? (Hint: Here the exponential term is too large to ignore. Use Newton's method to approximate the time t when the object...
A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface, as shown in Figure 5. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the f...
A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface, as shown in Figure 5. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant (a) (b) (c) (d) Calculate the total energy expended in the acceleration. Plot a graph of the kinetic...
Q3:- Body will be free vibrate from rest and distance Im under action of force f(t) = 3 sint by used second order differential equation find the equation of motion and find distance at t - 1 sec. Given (m= 1 kg & k= 4 N.m). Solution:-
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
Q3) A mass of 3 kg moves horizontally along x axis under the action of a force depends on time , given as following: F(t)4N where t in seconds, a) Find the impulse of this force during the interval t= 0 to t-2 S, if the mass starts motion from rest at x-0 b) Find its velocity and position as function of time.
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...
GROUP PROBLEM-1 SAN FRANCISCO STATE UNIVERSITY Given: The 300-kg bar B, originally at rest, is towed over a series of small rollers. The motor M is drawing in the cable at a rate of v (0.4 t2) m/s, where t is in seconds. Find: Force in the ca ble and distance s whent 5s. Plan: Since both forces and velocity are involved, this problem requires both kinematics and the equation of motion. 1) Draw the free-body and kinetic diagrams of...
The wheel shown in the diagram starts from rest under the
application of the constant force P=10 N. The wheel has a mass of
m=3 kg and a radius of gyration about its center of mass of and
kinetic coefficients of friction between the wheel and the inclined
plane are At the instant shown, the center of the wheel, G, has a
speed of 2 m/s. . The static and . (4 marks) (5 marks) (7 marks) (4
marks) a)...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
An object of mass 700 kg is released from rest 1000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b=50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? (Hint: Here the exponential term is too large to ignore. Use Newton's method to approximate the time t when the object...
A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface, as shown in Figure 5. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant (a) (b) (c) (d) Calculate the total energy expended in the acceleration. Plot a graph of the kinetic...
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