Physics Energy Unit

A force F at an angle θ above the horizontal is used to pull a heavy suitcase of weight mg a distance d along a level floor at constant velocity. The coefficient of friction between the floor and the suitcase is µ. The work done by the frictional force is:

(A) -Fd cos θ (Constant velocity F net =0, f k = Fx = Fcos θ W fk = - f k d = - Fcos θ d)

A force of 10 N stretches a spring that has a spring constant of 20 N/m. The potential energy stored in the spring is:

(A) 2.5 J (Two step problem. Do F = k∆x, solve for ∆x then sub in the U sp = ½ k∆x 2)

An automobile engine delivers 24000 watts of power to a car's driving wheels. If the car maintains a constant speed of 30 m/s, what is the magnitude of the retarding force acting on the car?

(A) 800 N (P = Fv, plug in to get the pushing force F and since its constant speed, F push = f k)

If the unit for force is F, the unit for velocity V, and the unit for time T, then the unit for energy is:

(A) FVT -(Try out the choices with the proper units for each quantity. Choice A ... FVT = (N) (m/s) (s) = Nm which is work in joules same as energy.)

A football is kicked off the ground a distance of 50 yards downfield. Neglecting air resistance, which of the following statements would be INCORRECT when the football reaches the highest point?

(A) all of the balls original kinetic energy has been changed into potential energy (At the top, the ball is still moving (v x ) so would still possess some kinetic energy)

A softball player catches a ball of mass m, which is moving towards her with horizontal speed V. While bringing the ball to rest, her hand moved back a distance d. Assuming constant deceleration, the horizontal force exerted on the ball by the hand is

(A) mV 2 /(2d) (The work done by the stopping force equals the loss of kinetic energy. -W=∆K - Fd = ½ mv f 2 - ½ mv i 2 v f = 0 F = mv 2 /2d)

A pendulum bob of mass m on a cord of length L is pulled sideways until the cord makes an angle θ with the vertical as shown in the figure to the right. The change in potential energy of the bob during the displacement is:

(A) mgL (1-cos θ) (The potential energy at the first position will be the amount "lost" as the ball falls and this will be the change in potential. U=mgh = mg(L-Lcos θ))

A rock is dropped from the top of a tall tower. Half a second later another rock, twice as massive as the first, is dropped. Ignoring air resistance,

(A) the distance between the rocks increases while both are falling. (Eliminating obviously wrong choices only leaves A as an option. The answer is A because since the first ball has a head start on the second ball it is moving at a faster rate of speed at all times. When both are moving in the air together for equal time periods the first faster rock will gain more distance than the slower one which will widen the gap between them.)

A mass m attached to a horizontal massless spring with constant k, is set into simple harmonic motion. Its maximum displacement from its equilibrium position is A. What is the masses speed as it passes through its equilibrium position?

(B) - A square root of k/m (Conservation of Energy, U sp = K, ½ kA 2 = ½ mv 2 solve for v)

A deliveryman moves 10 cartons from the sidewalk, along a 10-meter ramp to a loading dock, which is 1.5 meters above the sidewalk. If each carton has a mass of 25 kg, what is the total work done by the deliveryman on the cartons to move them to the loading dock?

(B) 3750 J (The work done must equal the total gain in potential energy 10 boxes * mgh (25)(10)(1.5) of each)

A compressed spring has 16 J of potential energy. What is the maximum speed it can impart to a 2 kg object?

(B) 4.0 m/s (The maximum speed would occur if all of the potential energy was converted to kinetic U = K 16 = ½ mv 2 16 = ½ (2) v 2)

A ball swings freely back and forth in an arc from point I to point IV, as shown. Point II is the lowest point in the path, III is located 0.5 meter above II, and IV is I meter above II. Air resistance is negligible. The speed of the ball at point II is most nearly

(B) 4.5 m/s (Apply energy conservation using points IV and II. U 4 = K 2 mgh = ½ mv 2)

A force F directed at an angle θ above the horizontal is used to pull a crate a distance D across a level floor. The work done by the force F is

(B) FD cos θ (A force directed above the horizontal looks like this θ To find the work done by this force we use the parallel component of the force (Fx) x distance. = (Fcos θ) d)

refer to the following situation: A car of mass m slides across a patch of ice at a speed v with its brakes locked. It the hits dry pavement and skids to a stop in a distance d. The coefficient of kinetic friction between the tires and the dry road isµ. If the car has a mass of 2m, it would have skidded a distance of

(B) d (Stopping distance is a work-energy relationship. Work done by friction to stop = loss of kinetic - f k d = - ½ mv i 2 µ k mg = ½ mv i 2 The mass cancels in the relationship above so changing mass doesn't change the distance)

A ball is thrown vertically upwards with a velocity v and an initial kinetic energy E k . When half way to the top of its flight, it has a velocity and kinetic energy respectively of

(B) v/root 2 , Ek/2 (Half way up you have gained half of the height so you gained ½ of potential energy. Therefore you must have lost ½ of the initial kinetic energy so E 2 = (E k /2). Subbing into this relationship E 2 = (E k /2) ½ mv 2 2 = ½ m v 2 / 2 v 2 2 = v 2 / 2 .... Sqrt both sides gives answer)

A mass, M, is at rest on a frictionless surface, connected to an ideal horizontal spring that is unstretched. A person extends the spring 30 cm from equilibrium and holds it by applying a 10 N force. The spring is brought back to equilibrium and the mass connected to it is now doubled to 2M. If the spring is extended back 30 cm from equilibrium, what is the necessary force applied by the person to hold the mass stationary there?

(C) 10 N (Based on F = k ∆x. The mass attached to the spring does not change the spring constant so the same resistive spring force will exist, so the same stretching force would be required)

A person pushes a box across a horizontal surface at a constant speed of 0.5 meter per second. The box has a mass of 40 kilograms, and the coefficient of sliding friction is 0.25. The power supplied to the box by the person is

(C) 50 W (Since the speed is constant, the pushing force F must equal the friction force f k =µF n =µmg. The power is then given by the formula P = Fv = µmgv)

A ball swings freely back and forth in an arc from point I to point IV, as shown. Point II is the lowest point in the path, III is located 0.5 meter above II, and IV is I meter above II. Air resistance is negligible. If the potential energy is zero at point II, where will the kinetic and potential energies of the ball be equal?

(C) At point III (Point IV is the endpoint where the ball would stop and have all U and no K. Point II is the minimum height where the ball has all K and no U. Since point III is halfway to the max U point half the energy would be U and half would be K)

If M represents units of mass, L represents units of length, and T represents units of time, the dimensions of power would be:

(C) ML2/ T3 (P = F d / t = (ma)d / t = (kg)(m/s 2 )(m) / (s) = kg m 2 / s 3)

A pendulum is pulled to one side and released. It swings freely to the opposite side and stops. Which of the following might best represent graphs of kinetic energy (E k ), potential energy (E p ) and total mechanical energy (E T )

(C) This is a conservative situation so the total energy should stay same the whole time. It should also start with max potential and min kinetic, which only occurs in choice C

A fan blows the air and gives it kinetic energy. An hour after the fan has been turned off, what has happened to the kinetic energy of the air?

(C) it turns into thermal energy (Total energy is always conserved so as the air molecules slow and lose their kinetic energy, there is a heat flow which increases internal (or thermal) energy)

A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, x min and x max . The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. Which graph can represent the kinetic energy of the block as a function of x ?

(D)

A box of old textbooks is on the middle shelf in the bookroom 1.3 m from the floor. If the janitor relocates the box to a shelf that is 2.6 m from the floor, how much work does he do on the box? The box has a mass of 10 kg.

(D) 130 J (The work done must equal the increase in the potential energy mgh = (10)(10)(1.3))

A 60.0-kg ball of clay is tossed vertically in the air with an initial speed of 4.60 m/s. Ignoring air resistance, what is the change in its potential energy when it reaches its highest point?

(D) 635 J (All of the K = ½ m v 2 is converted to U. Simply plug in the values)

A 3 kg block with initial speed 4 m/s slides across a rough horizontal floor before coming to rest. The frictional force acting on the block is 3 N. How far does the block slide before coming to rest?

(D) 8.0 m (The work done by friction equals the loss of kinetic energy - f k d = ½ mv f 2 - ½ mv i 2 v f = 0, plug in values to get answer)

Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring?

(D) The maximum kinetic energy and maximum potential energy are equal, but occur at different times. (For a mass on a spring, the max U occurs when the mass stops and has no K while the max K occurs when the mass is moving fast and has no U. Since energy is conserved it is transferred from one to the other so both maximums are equal)

A block of mass m slides on a horizontal frictionless table with an initial speed v o . It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed from its natural length?

(D) root m/k times v0 (Simple energy conservation K=U sp ½ mv o 2 = ½ k ∆x 2 solve for ∆x)

A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, x min and x max . The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. Which graph can represent the total mechanical energy of the blockspring system as a function of x ?

(E)

A horizontal force F is used to pull a 5kilogram block across a floor at a constant speed of 3 meters per second. The frictional force between the block and the floor is 10 newtons. The work done by the force F in 1 minute is most nearly

(E) 1,800 J (Since the speed is constant, the pushing force F must equal the friction force (10 N). The distance traveled is found by using d = vt = (3)(60 sec), and then the work is simply found using W=Fd)

refer to the following situation: A car of mass m slides across a patch of ice at a speed v with its brakes locked. It the hits dry pavement and skids to a stop in a distance d. The coefficient of kinetic friction between the tires and the dry road isµ. If the car has a speed of 2v, it would have skidded a distance of

(E) 4 d (Same relationship as above ... double the v gives 4x the distance)

An ideal spring obeys Hooke's law, F = kx. A mass of 0.50 kilogram hung vertically from this spring stretches the spring 0.075 meter. The value of the force constant for the spring is most nearly

(E) 66 N/m (Force is provided by the weight of the mass (mg). Simply plug into F=k∆x, mg=k∆x and solve)

The figure shows a rough semicircular track whose ends are at a vertical height h. A block placed at point P at one end of the track is released from rest and slides past the bottom of the track. Which of the following is true of the height to which the block rises on the other side of the track?

(E) It is between zero and h; the exact height depends on how much energy is lost to friction. (Since the track is rough there is friction and some mechanical energy will be lost as the block slides which means it cannot reach the same height on the other side. The extent of energy lost depends on the surface factors and cannot be determined without more information)

From the top of a high cliff, a ball is thrown horizontally with initial speed v o . Which of the following graphs best represents the ball's kinetic energy K as a function of time t ?

(E) curved starts above 0 (Since the ball is thrown with initial velocity it must start with some initial K. As the mass falls it gains velocity directly proportional to the time (V=Vi+at) but the K at any time is equal to 1/2 mv 2 which gives a parabolic relationship to how the K changes over time.)

A mass m is attached to a spring with a spring constant k. If the mass is set into motion by a displacement d from its equilibrium position, what would be the speed, v, of the mass when it returns to equilibrium position?

(E) d x root k/m (Same as question #1 with different variables used)

A weight lifter lifts a mass m at constant speed to a height h in time t. What is the average power output of the weight lifter?

(E) mgh /t (The force needed to lift something at a constant speed is equal to the object weight F=mg. The power is then found by P = Fd / t = mgh / t)

A construction laborer holds a 20 kg sheet of wallboard 3 m above the floor for 4 seconds. During these 4 seconds how much power was expended on the wallboard?

(E) none of these (P = Fd / t. Since there is no distance moved, the power is zero)

A 2 kg ball is attached to a 0.80 m string and whirled in a horizontal circle at a constant speed of 6 m/s. The work done on the ball during each revolution is:

(E) zero (In a circle moving at a constant speed, the work done is zero since the Force is always perpendicular to the distance moved as you move incrementally around the circle)