An object moving in a liquid experiences a linear drag force: F → d r a g = ( bv , direction opposite the motion), where b is a constant called the drag coefficient . For a sphere of radius R , the drag constant can be computed as b = 6p?R , where ? is the viscosity of the liquid. a. Find an algebraic expression for v x ( t ), the x -component of velocity as a function of time, for a spherical particle of radius R and mass m that is shot horizontally with initial speed v 0 through a liquid of viscosity ? . b. Water at 20°C has viscosity ? = 1.0 × 10-3 N s/m 2 . Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of 20°C water. How long will it take for the horizontal speed to decrease to 50% of its initial value?
An object moving in a liquid experiences a linear drag force: F → d r a g = ( bv , direction opposite the motion), where b is a constant called the drag coefficient . For a sphere of radius R , the drag constant can be computed as b = 6p?R , where ? is the viscosity of the liquid. a. Find an algebraic expression for v x ( t ), the x -component of velocity as a function of time, for a spherical particle of radius R and mass m that is shot horizontally with initial speed v 0 through a liquid of viscosity ? . b. Water at 20°C has viscosity ? = 1.0 × 10-3 N s/m 2 . Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of 20°C water. How long will it take for the horizontal speed to decrease to 50% of its initial value?
An object moving in a liquid experiences a linear drag force:
F
→
drag = (bv, direction opposite the motion), where b is a constant called the drag coefficient. For a sphere of radius R, the drag constant can be computed as b = 6p?R, where ? is the viscosity of the liquid.
a. Find an algebraic expression for vx(t), the x-component of velocity as a function of time, for a spherical particle of radius R and mass m that is shot horizontally with initial speed v0through a liquid of viscosity ?.
b. Water at 20°C has viscosity ? = 1.0 × 10-3 N s/m2. Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of 20°C water. How long will it take for the horizontal speed to decrease to 50% of its initial value?
A student suggests that the force of air resistance FA depends on the relative speed of an object passing
through the air v according to FA = kvN, where k is a constant with appropriate units that depends on
properties of the air and the size and shape of the object and N is a dimensionless exponent. The student
has a hollow ball made of two hemispherical shells that can be connected together and disconnected,
along with access to other commonly available materials. Write an experimental procedure that the
student could follow to make measurements in order to find the value of N, and explain how a graph of
In(FA) vs. In(v) could be used to find the values of k and N.
r
The speed of a boat in still water is V. A river flows with a speed of v₁. The boat travels distance of 14
miles downstream in a river in 1 hour. However, the return journey takes 2 hours. Calculate the V
and V₁.
Hint: Velocity = displacement/time. Displacement can be positive of neagtive depending on the
direction. You will first need to set up the equations by taking into account the resultant velocity of
the boat in flowing water. Consider the direction the river is flowing to be positive.
Set up two equations, one for the downstream journey and one for the upstream journey, in terms of
"V" and "v":
Do V" and "v, add or substract downstream to give the resultant downstream velocity?
Do v" and "v, add or substract upstream togive the resultant upstream velocity? Use the upstream
direction as negative. The resultant upstream velocity should be negative.
Equation 1 (downstream):
Equation 2 (upstream):
Solve for:
V₁²
vb
Write an algebraic expression; do not use numerical values except…
n object starts from origin att%3D0 moves along the x-
axis. the velocity of the object as a function of time is
shown in the in following figure. Find the average
velocity of the object between t%3D0S and t= 2s
4.0
v(m/s)
0 1 2 34 5 6
t(s)
Chapter 6 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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