SPH 4UMomentum and Energy Review
1.One of our alpine ski team members with a mass of 75 kg goes 500 m down a hill where the vertical drop is 300 m. If the speed changed from 10 m/s at the top to a mere 15 m/s at the bottom, what was the average force of friction? (432 N)
2.a)What does the force : extension graph look like for a Hooke’s Law spring?
b)What does the area beneath the curve represent?
c)If the spring were to reach its elastic limit, how does the graph change?
d)What would happen to the spring if it was stretched beyond this limit?
e)Why can’t you drop a mass attached to a spring to find the k – value?
3.In a new, yet much maligned, house league event, advanced spring compression, you jump from a height of 3.0 m onto a vertical ideal spring that has a spring constant of k = 2000 N/m.
Use g = 10 N/kg.
a)If your mass is a whopping 80.0 kg, what is the maximum compression of the spring?(2.0 m)
b)How fast would you be going when the spring is compressed only 1.0 m?(7.4 m/s)
4.A 175 g air-track glider is moving with a velocity of 8.0 m/s on a frictionless track and collides with an identical stationary glider, which is attached to a long ideal spring. The gliders remain attached and compress the spring 15 cm before coming to a stop.
a)What is the speed of the gliders immediately after impact? (4 m/s)
b)What is the spring constant of the ideal spring? (250 N/m)
c)How fast are the masses going when the spring is compressed 7.5 cm? (3.46 m/s)
5.A 20 g bullet travelling at 450 m/s hits a 9.0 kg mass that is free to swing on four long ropes (a ballistics pendulum). The bullet remains embedded in the mass and swings smoothly to its maximum height. Ignore any frictional effects.
a)What is the speed of the mass immediately after impact?(v = 1.0 m/s)
b)What is the elasticity of this collision?(e = 0.0022)
c)To what height above its initial position does it rise?(h = 0.051 m)
6.A 1000 kg Honda going West at 20 m/s has a one-dimensional collision (rear ends) a 2000 kg Ford van that is going West at 10 m/s. If 10% of the initial kinetic energy is converted to other forms of non-mechanical energy during the collision, what are the velocities of the car and the van after the collision? (vcar = 11.2 m/s [W], vvan = 14.4 m/s [W])
7.A 2.0 kg mass with a velocity to the right of 3.0 m/s collides with a 4.0 kg mass that has a velocity of 2.0 m/s to the left. If one half of the kinetic energy is lost during the collision, which is in one dimension, what are the velocities of the two masses after collision? ( 2.7 m/s, 0.83 m/s)
8.A 3.0 kg mass moving north at 1.0 m/s collides with a 2.0 kg mass moving east at 2.0 m/s. After the collision the 3.0 kg mass moves at 1.2 m/s in a direction E 7° N.
a)What is the velocity of the 2.0 kg mass after collision?(1.3 m/s E 81°N)
b)Is the collision elastic?(no)
9.Consider a collision in a two-dimensional horizontal plane. Mass A, 2.0 kg, is moving east at 4.0 m/s and hits mass B, 1.0 kg, which is moving west at 6.0 m/s. After the collision mA has a velocity of vA’ = 3.0 m/s [E 20° N]. Calculate the velocity of mB after the collision. Determine the elasticity of the collision.
(4.2 m/s 29.4°from vB or S 61° W; e = 0.52)
10.Under testing, an ideal spring vertically compresses 7.5 cm when under a 120 kg load.
a)What is the spring constant of the ideal spring?
The same spring (uncompressed) is then attached between a wall and a stationary 2.0 kg black glider on a track (Fig. 1). Another red glider of mass 4.0 kg slides from the position shown and impacts the black glider in an inelastic collision, compressing the spring. Assume that the track is frictionless everywhere, and that the two gliders stick together.
b)Determine the speed of the red glider just before impact.
d)What is the speed of each glider immediately after impact?
e)Calculate the maximum compression of the spring.
c)How fast is the black glider going when the spring is compressed to only 4.0 cm?
A toughie…
11.A light platform, that is attached to a long ideal spring, when suspended stationary is 1.30 m below the top of a scaffolding. Brendan drops his 55 kg mass onto the platform and continues down until he is 2.85 m below the top of the scaffold and momentarily stationary.
a)What is the initial Ee of the spring at the bottom?(1.54 kJ)
b)What is the spring constant?(1.28 x 103 N/m)
c)How fast will Brendan be going when he is 1.95 m below his initial position (the top of the scaffold)? (5.33 m/s)
Part B:Multiple Choice
- One end of a Hooke’s Law Spring is attached to a support and the other end is free. It is found that 50 J of work is needed to pull the free end 0.30 m from it rest position. How much additional work, in Joules, is required to pull the free end an additional 0.60 m?
a) 400b)300c)200d)100e)50
- As a result of the compression of a spiral spring, U units of potential energy are added to it. When this spring is allowed to return by of the distance it was compressed, its remaining potential energy in the same units will be
a) Ub) Uc)Ud) Ue)U
- Whenever a body strikes a stationary body of equal mass
a)the two bodies cannot stick togetherd)the collision must be elastic
b)total energy of all kinds is not conservede)momentum is necessarily conserved
c)the body that was originally moving must stop
- Which one of the following would describe a perfectly elastic collision between bodies?
a) Momentum is transferred from one body to another, but no kinetic energy is transferred from one body to another.
b)Total kinetic energy is the same after the collision as before, and total momentum is the same after the collision as before.
c)Total kinetic energy is the same after the collision as before, but total momentum is not the same after the collision as before.
d)Total kinetic energy is not the same after the collision as before, and total momentum is the same after the collision as before.
e)
Total momentum is the same after the collision as before, and there is no deformation of either body during the collision.
- The ball of mass 2.0 kg moving with a horizontal velocity of 5.0 m/s to the right hits a vertical wall and rebounds with a horizontal velocity of 4.0 m/s to the left, as shown in the diagram. The magnitude of the impulse on the ball is, in kgm/s
a)2.0b)5.0c)9.0d)10e)18
- A 75 kg man was riding on a 30 kg cart travelling at a speed of 2.0 m/s relative to the ground. He jumped off in such a way that he landed on the ground with a horizontal speed of 2.0 m/s in the same direction as the cart. What was the resulting change in the speed of the cart?
a)0 b) 3.0 m/sc)7.0 m/sd)2.0 m/se)5.0m/s
- The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m, m = 2.0 kg
a)3.7 m/s b)4.4 m/sc)4.9 m/sd)5.4 m/se)14 m/s
- Identical masses m are attached to identical springs of spring constant k suspended from the ceiling. With both masses hanging in their equilibrium positions, mass A is pulled down 10 cm and released, while mass B is pushed up 10 cm and released. Which is correct?
a)Mass A will travel a smaller distance to its highest point than mass B will travel to its lowest point.
b)Mass A will travel a greater distance to its highest point than mass B will travel to its lowest point.
c)Masses A and B will travel equal distances between their highest and lowest points.
d)More work was done on mass A by the extending force than on mass B by the compressing force.
e)The total work done on mass A by the extending force was equal to the total work done on mass B by the compressing force.
- Two objects have the same momentum but do not have the same mass. Consider the following statements about them:
I.The one with less mass has more kinetic energy.
II.The same work was done to accelerate each from rest.
III.Both deliver the same impulse when stopped.
Which of the above statements is/are correct?
a)I onlyd)I and III only
b)II onlye)II and III only
c)III only
- Whenever a body strikes a stationary body of equal mass
a)the two bodies cannot stick togetherd)the collision must be elastic
b)the body that was originally moving must stope)momentum is necessarily conserved
c)total energy of all kinds is not conserved
- Bob has two balls. He releases one ball from a platform of height H. Just as that ball strikes the ground, he releases the next ball from the same height. Assuming that the first ball bounces perfectly,( i.e., reversing only the direction of its velocity when it strikes the ground), at what height from the ground do the balls strike each other?
a)H/4 b) H/3c) H/2d)3H/4e)none of the above
- A body of mass 8.0 kg is moving due east with a speed of 5.0 m/s. It explodes into two parts having masses of 5.0 kg and 3.0 kg. Just after the explosion, the 3.0 kg mass has a velocity of 10 m/s [E] relative to the Earth’s surface. The speed of the 5.0 kg mass relative to the Earth’s surface will be, in m/s, most nearly
a)5.0b)4.0c)3.0d)2.0e)1.0
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