Download Hooke`s Law Problems

SPH 4U
Hooke’s Law Problems
1. The force applied to a dynamics cart is measured with a stretched spring. What is the
acceleration of a 2.0 kg cart on a flat, frictionless surface if pulled by a spring, of
force constant 40 N/m, stretched by a constant amount of 8.0 cm?
(1.6 m/s2)
2. What is the force constant of a Hooke's Law spring if the extension of the spring is
0.15 m when 0.72 J of potential energy is stored in it?
(64 N/m)
3. A 5.0 g pellet is placed in the barrel of a toy gun and is propelled by a spring of force
constant 50 N/m that has been compressed 20 cm and then released. Calculate the
maximum velocity of the pellet when shot horizontally.
(20 m/s)
4. The force-deformation graph for a non-Hooke's
Law spring is shown.
(a) How much work must be done to compress
the spring 0.16 m?
(b) How much potential energy is stored in the
spring at this compression?
(c) What speed would a 1.0 kg mass acquire if it
were placed next to this compressed spring,
on a smooth, horizontal surface, and then
released?
(0.72 J, 0.721 J, 1.2 m/s)
5. The spring in a toy gun has a force constant of
500 N/m. It is compressed 5.0 cm, and a ball of mass 10 g is placed next to it in the
barrel.
(a) What is the ball's maximum velocity, when the trigger releases the spring? Assume
that there is no friction, and that the gun barrel is level. (11 m/s)
(b) Determine the muzzle velocity if an average retarding force of 0.80 N acts on the
ball, and the barrel is 0.25 m long. (9.2 m/s)
6. A 3.0 kg ball is dropped from a height of 0.80 m onto a vertical spring of force
constant 1200 N/m. What is the maximum compression of the spring? (0.22 m)
7. A linear elastic spring is 15.0 cm long. When the upper end is held in the hand and a
500 g mass is suspended from the lower end, its length becomes 22.0 cm. If the hand
is now jerked quickly upward, the spring first extends to a length of 28.5 cm; then the
mass starts to move up. The hand is then held still.
(a) Calculate the acceleration with which the mass first begins to move. (9.1 m/s2)
(b) Calculate the speed of the mass when the length of the spring is 22.0 cm again.
(0.77 m/s)
(c) Calculate the length of the spring when the mass comes to rest at its highest point.
(15.5 cm)
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