For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed v i . Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: F → net = − m k v 2 i ^ , where k is a constant. The speed of the object after t = 0 is given by v = v i /(1 + kv i t ). (a) Find the position x of the object as a function of time. (b) Find the object’s velocity as a function of position.
For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed v i . Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: F → net = − m k v 2 i ^ , where k is a constant. The speed of the object after t = 0 is given by v = v i /(1 + kv i t ). (a) Find the position x of the object as a function of time. (b) Find the object’s velocity as a function of position.
Solution Summary: The author explains the position of the object in terms of time, the net resistive force, and the expression for the speed of an object.
For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed:
F
→
net
=
−
m
k
v
2
i
^
, where k is a constant. The speed of the object after t = 0 is given by v = vi/(1 + kvit). (a) Find the position x of the object as a function of time. (b) Find the object’s velocity as a function of position.
For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: net = −mkv2î, where k is a constant. The speed of the object after t = 0 is given by
v = vi/(1 + kvit).
(a) Find the position x of the object as a function of time. (Use the following as necessary: k, m, t, and vi.)x(t) =
(b) Find the object's velocity as a function of position. (Use the following as necessary: k, m, t, vi, and x.)
v(t)=
The force acting on a particle is F - (10x – 17) N, where x is in meters.
(a) Make a plot of this force versus x from x = 0 to x = 3.00 m.
F (N)
F (N)
20
50
40
10-
30
0,5
20
1.0
20
25
x (m)
30
-10
10
atx (m)
3.0
0.5
1.0
1.5
2.0
2.5
F (N)
F (N)
0,5
1.0
1,5
2.0
2.5
x (m)
30
10
-10
-20
0,5
15
x (m)
30
10
2.5
-30
-10
-40
-50
-20
(b) From your graph, find the net work done by this force on the particle as it moves from x = 0 to x= 2.55 m. (Include the correct sign.)
An object with mass m = 34 kg is pushed with 452 N of force to be moved across a distance of 4.6 m on a surface with friction. Initially the object is moving at vi = 0.82 m/s and after being moved across 4.6 m, the final speed is 2.5 m/s. What is the magnitude of the frictional force acting on the object in the unit of N?
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