1.A brick of mass m initially traveling at speed vo slows to a stop while sliding along a rough horizontal surface. m=7.5 kg, vo=25 m/s a)What is the work done by the frictional force in stopping the brick? b)If the brick slides for 33 m before coming to rest, find μk, the coefficient of kinetic friction between the brick and the surface.
1.A brick of mass m initially traveling at speed vo slows to a stop while sliding along a rough horizontal surface. m=7.5 kg, vo=25 m/s
a)What is the work done by the
b)If the brick slides for 33 m before coming to rest, find μk, the coefficient of kinetic friction between the brick and the surface.
2.A variable force acts on a mass of 1.2 kg as it moves in one dimension along the x-axis. The force is position-dependent and is given by the equation:
F(x) = (5 N/m) x + 3 N.
Assume there are no other forces acting on the mass.
a)How much work is done by this force in moving the mass from x = 1 m to x = 4 m?
b)If the kinetic energy of the mass is 50 J at x = 1 m, what is the kinetic energy of the mass when it reaches x = 4 m?
c)What is the velocity of the mass when it reaches x = 4 m?
4.A puck starts from rest at point A and slides on the frictionless path shown. It is launched horizontally off the end of the track and lands on the ground below.
hA=20 m
hB=10 m
hC=4 m
a)What is the speed of the puck at point B?
b)What is the speed of the puck at point C, as it is launched off the end of the track?
c)What is the speed of the puck at point C if 75 J of energy is dissipated by the forces of friction and air resistance as the puck moves from A to C? The puck has a mass m=0.5 kg.
6.A cannon can launch an artillery shell with an initial launch speed of 320 m/s. (Solve the following problems using energy considerations, and ignoring air resistance)
a)If the shell is launched vertically upward, how high will the shell go above its launch position?
b)When a 100kg shell is at half of its maximum height, what is its kinetic energy?
c)If the shell is launched with the same speed, but at an angle of 65˚ with respect to the horizontal, how high will it go above its launch position? Keep in mind that the kinetic energy will not be zero at the high point of the trajectory.
5.Consider a horizontal block-on-a-spring problem. The block has a mass m=600 g and the spring has a spring constant k=300 N/m. Assume no friction in this problem.
a)Find the total mechanical energy stored in the system when the block is displaced 1.50 m from the equilibrium position and held in place.
b)If the block is released from the 1.50 m displacement, what is its speed when it is 0.75 m from equilibrium?
6.A block of mass m is placed (at rest) against a locked, compressed spring as shown. The spring has been compressed a distance x from its equilibrium length. The spring constant is k. The spring lock is then released and propels the block up the incline. How far up the incline will the block move when the spring lock is released? Assume there is no friction in the problem.
m=0.75 kg
x=0.04 m
k=80000 N/m
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θ=24°
7.A block starts from rest at position A and slides on the track shown, coming to rest at position C. The track is frictionless except for a portion of length L between points B and C where the coefficient of kinetic friction between the block and the track is k. Find the height, h, of point A above point C.
L=1.5m
μk= 0.80
8.A simple pendulum consisting of a bob of mass m attached to a massless string of length L is displaced an angle θ from the vertical and released from rest. What is the speed of the bob as it passes through the lowest point in its path?
m=20 g
L=25 cm
θ=16°
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