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SPH 4U
Conservation of Energy Problems
Conservation
1.
A 2.0 kg mass is placed against a spring of force constant 800 N/m, which has been compressed
0.22 m, as illustrated. The spring is released, and the object moves along the horizontal,
frictionless surface and up the slope.
Calculate:
(a) the maximum elastic potential energy of the spring
(b) the maximum velocity of the mass
(4.4 m/s)
(c) the maximum vertical height of the mass, up the slope
(19 J)
(1.0 m)
2. A ball bearing of mass 50 g is sitting on a vertical spring whose force constant is 120 N/m. By
how much must the spring be compressed so that, when released, the ball rises to a maximum
height of 3.1 m above its release position? (0.16 m)
3. A 30 kg girl goes down a slide, reaching the bottom with a velocity of 2.5 m/s. The length of the
slide is 10.0 m and the top end is 4.0 m above the bottom end, measured vertically.
(a) What is her gravitational potential energy at the top of the slide, relative to the bottom?
(b) What is her kinetic energy when she reaches the bottom?
(c) How much energy is lost due to friction?
(d) Calculate the average frictional force acting on her as she goes down the slide.
(1.2 x 103 J, 94 J, 1.1 x 103 J, -1.1 X 102 N)
4. A 1.0 kg lead sphere is suspended from the ceiling by a wire 5.0 m long. The ball is pulled
sideways and up, until the wire is horizontal, and then released. Find:
(a) the maximum velocity acquired by the ball
(9.9 m/s)
(b) the tension in the wire at the lowest point in the swing
(29 N)
5. A uniform bar of iron is supported by a long,
uniform Hooke's Law spring as shown in A. The
spring is cut exactly in half and the two pieces
are used to support the same bar, as shown in B.
If the whole spring stretched by 4 cm in A, by
how much would each half spring stretch in B?
(SIN '69)
(1 cm)
p. 211 #8, 9, 10, 11, 13
p. 219 #10, 13
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SPH 4U
1.
(a)
(b)
(c)
(d)
Momentum and Energy Problems
A bullet's speed may be determined by firing it into a sandbag pendulum,
and measuring the vertical height to which the pendulum rises, as shown.
(The bullet stays in the sandbag.)
What is the change in gravitational potential energy of the sandbag and
bullet during the swing?
What is the velocity of the sandbag-bullet combination at the start of
the swing?
What is the original velocity of the bullet?
Is the collision between the bullet and the sandbag elastic or inelastic?
(3.9 J, 0.89 m/s, 4.5 X 102 m/s)
2. Isaac Newton was not inspired by an apple falling on his head. Actually, he was lying down and
the apple struck his stomach. It then bounced straight back up, having lost 10% of its kinetic
energy in the collision. How high did it rise on the first bounce if it had originally dropped from
a branch 1.0 m above Isaac's stomach? (SIN '72)
(0.90 m)
3. Realizing that he could not drive up a 30°, ice-covered hill because there was no friction, Sir
Isaac Newton had stopped his cart, of total, mass 500 kg, at the bottom. He was struck in the
rear by a London stage coach, of total mass 1500 kg, travelling at 20 m/s. The two vehicles
stuck together, with nothing breaking loose, and slid up the hill in a straight line. How far up the
slope did the wreckage get before coming to rest? (SIN '70)
(23 m)
4. Tarzan is hanging on the end of a vine, at point A, over an alligator-infested river. He must
reach point B, in a tree, to be safe. Tarzan's monkey, Cheetah, located at C in a nearby tree,
jumps, and is moving horizontally when Tarzan catches him. Given the following data, calculate
the minimum horizontal speed, v, of the monkey, necessary for the two to reach safety. Length
of vine = 30 m; mass of Tarzan = 75 kg; mass of monkey = 25 kg.
(36 m/s)
5. A very light basket hangs from the limb of a tree by a long spring. The limb extends out over a
pond, and the spring holds the basket 3.0 m above the surface of the pond. Three girls of equal
mass carefully lower themselves into the basket, one after the other, causing the spring to
stretch 1.0 m for each additional girl, so that with all three aboard, the basket just touches the
water. The girls then jump into the water, and the basket returns to its original position. Once
back on shore, one of the girls climbs to a higher limb of the tree and steps off, landing in the
basket and causing the spring to stretch until the basket just touches the water's surface
again, for an instant. From what height above the water's surface did the girl step from the
higher limb? (SIN '73)
(4.5 m)
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