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Exam 7: Potential Energy and Energy Conservation

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Question 21

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A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of .What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

A) 26.0 m/s
B) 27.4 m/s
C) 28.7 m/s
D) 26.7 m/s
E) 28.1 m/s

F) A) and D)
G) A) and B)

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Question 22

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Swimmers at a water park have a choice of two frictionless water slides as shown in the figure.Although both slides drop over the same height,h,slide 1 is straight while slide 2 is curved,dropping quickly at first and then leveling out.How does the speed v₁ of a swimmer reaching the end of slide 1 compares with v₂,the speed of a swimmer reaching the end of slide 2?

A) v₁ > v₂
B) v₁ < v₂
C) v₁ = v₂
D) No simple relationship exists between v₁ and v₂ because we do not know the curvature of slide 2.

E) A) and B)
F) A) and C)

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Question 23

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A force on an object is given by F(x)= (2.00 N/m)x - (3.00 N/m³)x³.What is a potential energy function U(x)for this conservative force?

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead use a spring having force constant 2k

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface.After being released from rest,the mass acquires a maximum speed v and a maximum kinetic energy K.If instead the mass initially compresses the spring twice as far,

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass.The platform drops 6.00 cm before the person comes to rest.What is the spring constant of the spring?

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long.You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest.What is your sister's mass,assuming negligible friction?

The only force acting on an object moving along the x-axis is the conservative force given by F(x)= (2.00 N/m)x + (1.00 N/m³)x³. (a)What is the change in potential energy when the object moves from x = 1.00 m to ? (b)What is the change in kinetic energy when the object moves from x = 1.00 m to ?

A ball drops some distance and gains 30 J of kinetic energy.Do NOT ignore air resistance.How much gravitational potential energy did the ball lose?

An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position,a distance of 6.4 cm below the starting point.If instead of having been lowered slowly the object was dropped from rest,how far then would it then stretch the spring at maximum elongation?

A car on a roller coaster starts at zero speed at an elevation above the ground of .It coasts down a slope,and then climbs a hill.The top of the hill is at an elevation of .What is the speed of the car at the top of the hill? Neglect any frictional effects.

An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0,as shown in the figure.A very small 4.0-kg ball is attached to the other end of the rod.The ball is held at A,where the rod makes a 30° angle above the horizontal,and is released.The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B.The tension in the rod when the ball passes through the lowest point at D is closest to

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end.The rod is held vertical,with the object at the top,and released,allowing the rod to swing.What is the speed of the object at the instant that the rod is horizontal?

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope and a uniform surface.When the skier reaches the bottom of the hill,her speed is . (a)How much work is done by friction as the skier comes down the hill? (b)What is the magnitude of the friction force if the skier travels directly down the hill?

Which,if any,of the following statements concerning the work done by a conservative force is NOT true?

Two identical balls are thrown directly upward,ball A at speed v and ball B at speed 2v,and they feel no air resistance.Which statement about these balls is correct?

When an object is solely under the influence of conservative forces,the sum of its kinetic and potential energies does not change.

Consider the motion of a 1.00-kg particle that moves with potential energy given by .Suppose the particle is moving with a speed of when it is located at x = 1.00 m.What is the speed of the object when it is located at ?

The potential energy for a certain mass moving in one dimension is given by .Find the location(s) where the force on the mass is zero.

A 1.37-kg block is held in place against the spring by a 74-N horizontal external force (see the figure) .The external force is removed,and the block is projected with a velocity upon separation from the spring.The block descends a ramp and has a velocity at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction over this section is 0.24.The velocity of the block is at C.The block moves on to D,where it stops.The initial compression of the spring is closest to