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Exam 7: Potential Energy and Energy Conservation

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Question 1

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A potential energy function is given by U(x)= (3.00 J)x + (1.00 J/m²)x³.What is the force function F(x)that is associated with this potential energy function?

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F(x)= -3.00 N - (3.00 N/m²)x²

Question 2

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A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³.The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³,where A is a positive quantity.How does the force on system 1 relate to the force on system 2 at a given position?

A) The force on the two systems will be in opposite directions.
B) The force is identical on the two systems.
C) The force on the second system will be with less than the force on the first system.
D) There is no relationship between the forces on the two systems.
E) The force on the second system will be with greater than the force on the first system.

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Question 3

Multiple Choice

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A block slides down a frictionless inclined ramp.If the ramp angle is 17.0° and its length is find the speed of the block as it reaches the bottom of the ramp,assuming it started sliding from rest at the top.

A 2.5-kg box,sliding on a rough horizontal surface,has a speed of 1.2 m/s when it makes contact with a spring (see the figure).The block comes to a momentary halt when the compression of the spring is 5.0 cm.The work done by the friction,from the instant the block makes contact with the spring until is comes to a momentary halt,is -0.50 J. (a)What is the spring constant of the spring? (b)What is the coefficient of kinetic friction between the box and the rough surface?

A 2.0-kg object is moving without friction along the x-axis.The potential energy curve as a function of position is shown in the figure,and the system is conservative.If the speed of the object at the origin is 4.0 m/s,what will be its speed at 7.0 m along the +x-axis?

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure.What is the length s of the ramp from A to B?

A spring-loaded dart gun is used to shoot a dart straight up into the air,and the dart reaches a maximum height of 24 meters above its point of release.The same dart is shot up a second time from the same gun,but this time the spring is compressed only half as far (compared to the first shot) .How far up does the dart go this time? (Neglect friction and assume the spring is ideal and massless.)

A girl throws a stone from a bridge.Consider the following ways she might throw the stone.The speed of the stone as it leaves her hand is the same in each case,and air resistance is negligible. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below?

An object of mass 4.0 kg starts at rest from the top of a rough inclined plane of height 10 m as shown in the figure.If the speed of the object at the bottom of the inclined plane is 10 m/s,how much work does friction do on this object as it slides down the incline?

A force on an object is given by F(x) = ( -4.00 N/m) x + ( 2.00 N/m³) x³.What is the change in potential energy in moving from to ?

Two stones,one of mass m and the other of mass 2m,are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance.Which statement about these stones is true?

In the figure,a 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall.After the block collides with the spring,the spring is compressed a maximum distance of 0.68 m.What is the speed of the block when it has moved so that the spring is compressed to only one-half of the maximum distance?

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

An 0.80-kg block is held in place against the spring by a 67-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 0.39.The velocity of the block is at C.The block moves on to D,where it stops.The spring constant of the spring is closest to

An 8.0-kg block is released from rest,with v₁ = 0.00 m/s,on a rough incline,as shown in the figure.The block moves a distance of 1.6-m down the incline,in a time interval of 0.80 s,and acquires a velocity of v₂ = 4.0 m/s.How much work does gravity do on the block during this process?

The plot in the figure shows the potential energy of a particle,due to the force exerted on it by another particle,as a function of distance.At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

In the figure,a block of mass m is moving along the horizontal frictionless surface with a speed of 5.70 m/s.If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260,how far does the block travel up the incline?

A 2.0 kg mass is moving along the x-axis.The potential energy curve as a function of position is shown in the figure.The kinetic energy of the object at the origin is 12 J.The system is conservative,and there is no friction. (a)What will be the kinetic energy at 2.0 m along the +x-axis? (b)What will be the speed of the object at 6.0 m along the +x-axis?

A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in the figure.The vertical height above ground level at position A is 200 m.Neglect friction. (a)What is the total mechanical energy of the roller coaster at point A? (b)What is the total mechanical energy of the roller coaster at point B? (c)What is the speed of the roller coaster at point B? (d)What is the speed of the roller coaster at point C?

In the figure,a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop.The radius of the track is 9.9 m and the mass of the car is 1800 kg.Find the magnitude of the force of the car on the track when the car is at point A.You can treat the car as a point mass.