An object of mass m is dropped from the roof of a building of height h . While the object is falling, a wind blowing parallel to the face of the building exerts a constant horizontal force F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h . (b) Find an expression in terms of m and F for the acceleration a x of the object in the horizontal direction (taken as the positive x -direction). (c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m , g , F , and h . (d) Find the magnitude of the object’s acceleration while it is falling, using the variables F , m , and g .
An object of mass m is dropped from the roof of a building of height h . While the object is falling, a wind blowing parallel to the face of the building exerts a constant horizontal force F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h . (b) Find an expression in terms of m and F for the acceleration a x of the object in the horizontal direction (taken as the positive x -direction). (c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m , g , F , and h . (d) Find the magnitude of the object’s acceleration while it is falling, using the variables F , m , and g .
An object of mass m is dropped from the roof of a building of height h. While the object is falling, a wind blowing parallel to the face of the building exerts a constant horizontal force F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h. (b) Find an expression in terms of m and F for the acceleration ax of the object in the horizontal direction (taken as the positive x-direction). (c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m, g, F, and h. (d) Find the magnitude of the object’s acceleration while it is falling, using the variables F, m, and g.
a block of mass m = 10.2 kg sitting on a ramp that makes an angle θ = 21° with the horizontal. This block is being pushed by a horizontal force F = 212 N. The coefficient of kinetic friction between the two surfaces is μ = 0.49. Write an equation for the acceleration of the block up the ramp using variables from the problem statement together with g for the acceleration due to gravity. Find the acceleration of the block up the ramp in m/s2.
A horizontal force of magnitude F = 57.5 N pushes on a block of mass m = 4.7 kg. The block is on a frictionless incline that makes and angle θ = 36.1 degrees with horizontal.
Write an expression for the acceleration ax of the block, taking up the ramp to be the positive x direction. Express your answer in terms of F, m, θ, and g (9.80 m/s2).
You drop an object of mass m from a tall building.
Suppose the only forces affecting its motion are
gravity, and air resistance proportional to the
object's speed with positive constant of
proportionality k. Let g denote gravitational
acceleration (a positive constant).
Express the total force in terms of m, g, and the
object's velocity v, where upward displacement is
considered positive.
F
=
mg - kv
Newton's second law tells us that force is equal to
mass x acceleration, F = ma. Relating
acceleration to velocity, rewrite the equation for
total force above as a first order differential
equation for v as a function of t. Denote v' as
dv
dt
v(t)
m(- dr)
this is not an equation.
Solve this differential equation for v(t) with the
initial condition v(0)
= V0.
=
mg (1-e ==)
m
k
Find the terminal
Terminal velocity =
mg
k
X
velocity.
X syntax error:
X
X
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