The position of a particle moving under uniform accelerationis some function of time and the acceleration....
The position of a particle moving under uniform accelerationis some function of time and the acceleration. Suppose we writethis position as: x=kamtn where k is adimensionless constant. Show by dimensional analysis that this expression is satisfied if m=1 and n=2. Can this analysis give the value of k?
a)Draw a picture
b)write down what you know
c)write down relevant equations
d)solve the unknown
e)Plug in numbers and calculate
f)units and direction
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The position of a particle moving under uniform accelerationis
some function of time and the acceleration....
2. A particle of mass m is moving in a plane under a force whose potential energy is given by V(r...
2. A particle of mass m is moving in a plane under a force whose potential energy is given by V(r) -kin r + cr + gr cos θ with k,c,g positive constants. (a) Write down the force in polar coordinates. (b) Find the positions of equilibrium (1) if c>g and (2) if c<g. (c) By considering the direction of the force near these points, determine whether the equilibrium is stable or not
2. A particle of mass m is...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same in...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
(a) Consider a particle which starts moving around from the origin in a 3-dimensional space. De- ...
(a) Consider a particle which starts moving around from the origin in a 3-dimensional space. De- termine the velocity vector v(t) in terms of φ and θ if it is constantly moving at the speed 5m/s, along the direction (φ,0). Here, φ denotes the angle between the z-axis and the projection of the position vector r(t) on the xy-plane; meanwhile θ denotes the angle between the z-axis and r(t). You may assume that (φ, θ) are fixed over time at...
Name: Show your work for full credit!!! 1. If the position function for a moving particle...
Name: Show your work for full credit!!! 1. If the position function for a moving particle is s(t) = (9 sin (5).-3 cos (5) + 1, 66°/2 + 4), where distances are in meters and r is in seconds, find the speed of the particle when t = 6. Give the simplified exact result or round accurately to 4 decimal places, and include the units with your answer. 2. A small spacecraft is maneuvering near an orbital space station. At...
Problem 7. A board of uniform size and composition sits horizontally on a support positioned unde...
Problem 7. A board of uniform size and composition sits horizontally on a support positioned under its center. The mass of the board is unknown. If there is a 20.0 kg mass is on the right hand end of the board what is the constant of the spring holding the other end of the board if it is stretched .500 m past its equilibrium position? (13 points) Do an extended free body diagram here What kind of problem is this?...
1. A particle is moving along a (horizontal) x-axis. Its position as a function of time...
1. A particle is moving along a (horizontal) x-axis. Its position as a function of time is given by the equationAt2 B where A-2.10 and B-2.80 and t is in seconds. (i) What are the proper units for A and B in SI units (show your work) (ii) Determine the displacement of the particle during the time interval from -3.00 s to 12 5.00 s. iii) Determine the average velocity (think secant line!) during this time interval (iv) Determine the...
4. A particle of mass m 2 kg moves under the potential energy function U(x.y.z)- (kx...
4. A particle of mass m 2 kg moves under the potential energy function U(x.y.z)- (kx + 2 k2y2 +3 k3z3) where k 1N. a. Suppose the particle has speed vo3 m/s when it passes through the origin. What will its speed be if and when it passes through the point (1,1.1)? b. Suppose the particle's speed vo at the origin is not known and that the point (1,1,1) is a turning point of the motion (a point where v0)....
4.0 m Question 4: A 2.0 kg particle slides down from rest from position A. When...
4.0 m Question 4: A 2.0 kg particle slides down from rest from position A. When it reaches B, it enters a rough horizontal segment with f4k-0.20, and eventually comes to rest at D. The surface from A to B is frictionless, and point A is located 4.0 m above the ground (a) Draw a free body diagram (FBD) for the particle at A (b) Draw a free body diagram (FBD) for the particle at C (c) Is the total...
PHYS 121 – Special Problem 1 Multiple Representations and Kinematics Two children are playing a game...
PHYS 121 – Special Problem 1 Multiple Representations and Kinematics Two children are playing a game where they run towards each other and see who can reach a toy that is somewhere between them. In the beginning, Charlie is 23.7 m away from the toy, running towards it at a speed of 0.770 m/s, and is speeding up. At the same time, Amy is 12.5 m away from the toy, is running towards it in the opposite direction as Charlie...
Example 4.3 A Bull's-Eye Every Time In a popular lecture demonstration, a projectile is fired at...
Example 4.3 A Bull's-Eye Every Time In a popular lecture demonstration, a projectile is fired at a target in such a way that the projectile leaves the gun at the same time the target is dropped from rest. Show that if the gun is initially aimed at the stationary target, the projectile hits the falling target as shown in figure (a). The velocity of the projectile (red arrows) changes in direction and magnitude, but its acceleration (purple arrows) remains constant....
2. A particle of mass m is moving in a plane under a force whose potential energy is given by V(r) -kin r + cr + gr cos θ with k,c,g positive constants. (a) Write down the force in polar coordinates. (b) Find the positions of equilibrium (1) if c>g and (2) if c<g. (c) By considering the direction of the force near these points, determine whether the equilibrium is stable or not
2. A particle of mass m is...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
(a) Consider a particle which starts moving around from the origin in a 3-dimensional space. De- termine the velocity vector v(t) in terms of φ and θ if it is constantly moving at the speed 5m/s, along the direction (φ,0). Here, φ denotes the angle between the z-axis and the projection of the position vector r(t) on the xy-plane; meanwhile θ denotes the angle between the z-axis and r(t). You may assume that (φ, θ) are fixed over time at...
Name: Show your work for full credit!!! 1. If the position function for a moving particle is s(t) = (9 sin (5).-3 cos (5) + 1, 66°/2 + 4), where distances are in meters and r is in seconds, find the speed of the particle when t = 6. Give the simplified exact result or round accurately to 4 decimal places, and include the units with your answer. 2. A small spacecraft is maneuvering near an orbital space station. At...
Problem 7. A board of uniform size and composition sits horizontally on a support positioned under its center. The mass of the board is unknown. If there is a 20.0 kg mass is on the right hand end of the board what is the constant of the spring holding the other end of the board if it is stretched .500 m past its equilibrium position? (13 points) Do an extended free body diagram here What kind of problem is this?...
1. A particle is moving along a (horizontal) x-axis. Its position as a function of time is given by the equationAt2 B where A-2.10 and B-2.80 and t is in seconds. (i) What are the proper units for A and B in SI units (show your work) (ii) Determine the displacement of the particle during the time interval from -3.00 s to 12 5.00 s. iii) Determine the average velocity (think secant line!) during this time interval (iv) Determine the...
4. A particle of mass m 2 kg moves under the potential energy function U(x.y.z)- (kx + 2 k2y2 +3 k3z3) where k 1N. a. Suppose the particle has speed vo3 m/s when it passes through the origin. What will its speed be if and when it passes through the point (1,1.1)? b. Suppose the particle's speed vo at the origin is not known and that the point (1,1,1) is a turning point of the motion (a point where v0)....
4.0 m Question 4: A 2.0 kg particle slides down from rest from position A. When it reaches B, it enters a rough horizontal segment with f4k-0.20, and eventually comes to rest at D. The surface from A to B is frictionless, and point A is located 4.0 m above the ground (a) Draw a free body diagram (FBD) for the particle at A (b) Draw a free body diagram (FBD) for the particle at C (c) Is the total...
Example 4.3 A Bull's-Eye Every Time In a popular lecture demonstration, a projectile is fired at a target in such a way that the projectile leaves the gun at the same time the target is dropped from rest. Show that if the gun is initially aimed at the stationary target, the projectile hits the falling target as shown in figure (a). The velocity of the projectile (red arrows) changes in direction and magnitude, but its acceleration (purple arrows) remains constant....
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