Two masses are arranged
as shown. Mass m1 has a mass
of 4.00 kg and is attached to the vertical surface on the left with a string in
which the tension is T. Mass m2
= 6.00 kg, is sitting on the horizontal surface and is being pulled to the right
by a force F, so that m2 is moving to the right at a constant speed.
The coefficient of sliding friction between m1 and m2
is μ1 = 0.380, while the coefficient of sliding friction between m2
and the horizontal surface is μ2 = 0.510.
(a) What will be the tension T in the string?
(b) What will be the magnitude of the force F required to pull m2 to the right at a constant speed?Solution:
that the earth were of uniform density and that a tunnel was drilled along a
diameter. If an object were dropped into the tunnel, show that it would
oscillate with a period equal to the period of a satellite orbiting the earth
just at the surface.
(b) Find the gravitational acceleration at a point P, a distance x from the surface of a spherical object of radius R. The object has density ρ. Inside the object is a spherical cavity of radius R/4. The center of this cavity is situated a distance R/4 beyond the center of the large sphere C, on the line from P to C.
A particle of mass m is given an initial velocity v0i.
Assume that the particle is subject to a drag force F = -bv½i.
(a) Find v as a function of time.
(b) How far does the particle travel before coming to rest?
A thrill-seeking student jumps off a bridge from the height H = 80.0 m above the water level. The student is attached to the bridge by an elastic cord so that she reaches zero velocity just as she touches the water. After some up-and-down bouncing, the student eventually comes to rest h = 20.0 m above the water level. What is the maximum speed reached by the student during the fall? Neglect air resistance and use 10.0 m/s2 for the acceleration due to gravity.
Assume a perfectly spherical Earth of radius R with a
frictionless surface. On the surface of this Earth an object with mass m is
moving with constant speed v towards the north pole. When the object is at
latitude λ, find the external force required to keep it moving on that
For m = 1 kg, v = 500 m/s, λ = 45o give a numerical answer.
MEarth = 5.97*1024 kg, REarth = 6378 km.