CP A holiday ornament in the shape of a hollow sphere with mass M = 0.015 kg and radius R = 0.050 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum with negligible friction. Calculate its period. ( Hint: Use the parallel-axis theorem to find the moment of inertia of the sphere about the pivot at the tree limb.)
CP A holiday ornament in the shape of a hollow sphere with mass M = 0.015 kg and radius R = 0.050 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum with negligible friction. Calculate its period. ( Hint: Use the parallel-axis theorem to find the moment of inertia of the sphere about the pivot at the tree limb.)
CP A holiday ornament in the shape of a hollow sphere with mass M = 0.015 kg and radius R = 0.050 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum with negligible friction. Calculate its period. (Hint: Use the parallel-axis theorem to find the moment of inertia of the sphere about the pivot at the tree limb.)
A block of mass m₁
=
10.0 kg is connected to a block of mass m₂
34.0 kg by a massless string that passes over a light, frictionless pulley. The 34.0-kg block is connected to a spring that has negligible mass and a force constant of k = 200 N/m as shown in the figure below. The spring is
unstretched when the system is as shown in the figure, and the incline is frictionless. The 10.0-kg block is pulled a distance h = 22.0 cm down the incline of angle = 40.0° and released from rest. Find the speed of each block when the spring is again unstretched.
Vm1
×
1.32
Vm2
= 1.32
×
m/s
m/s
A block of mass m₁ = 10.0 kg is connected to a block of mass m₂ = 34.0 kg by a massless string that passes over a light, frictionless pulley. The 34.0-kg block is connected to a spring that has negligible mass and a force constant of k = 200 N/m as shown in the figure below. The spring is
unstretched when the system is as shown in the figure, and the incline is frictionless. The 10.0-kg block is pulled a distance h = 22.0 cm down the incline of angle 0 = 40.0° and released from rest. Find the speed of each block when the spring is again unstretched.
m/s
Vm1
Vm2
m/s
mi
m2
k
i
Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as in the figure below. The helper spring engages when the main leaf spring is compressed by distance yo, and then helps to
support any additional load. Consider a leaf spring constant of 5.45 × 105 N/m, helper spring constant of 3.60 × 105 N/m, and y = 0.500 m.
Truck body
Dyo
Axle
(a) What is the compression of the leaf spring for a load of 4.90 × 105 N?
m
(b) How much work is done compressing the springs?
]
Chapter 14 Solutions
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