Exam #1 2001

(A) What is the acceleration of the car in SI units?
Ans:{-.142 m/s²}

(B) What is the car’s speed when it stops breaking?
Ans:{19.7 m/s}

(C) How long does the car brake?
Ans:{7.89 s}

(A) What are the SI units of a and b?
Ans:{a -> m/s, b -> m/s²}

(B) Determine the equation for the particle’s instantaneous speed as a function of time and calculate its speed at t = 2.50 seconds?
Ans:{}

(C) At what speed will the particle have an acceleration of 0.000 m/s²?
Ans:{2.45m/s}

(A) What is the vertical speed of the ball at 1.50 seconds?
Ans:{7.17 m/s}

(B) How far horizontally is the ball from its launch position at 1.50 seconds?
Ans:{37.5 m/s}

(C) With what speed was the ball launched from the ground?
Ans:{33.2 m/s}

(A) What is the heading of the boat relative to the bank?
Ans:{31.0^o}

(B) What is the speed of the boat in still water?
Ans:{9.19 cm/s or .331 km/hr}

(C) How far down river will the boat land when it reaches the other bank relative to the start point projected across the to the opposite side?
Ans:{2.01 km}

Exam #1 1999

(A) How fast is the car moving in m/s after it accelerates for 75.0 s, i.e., what is the final speed of the car in m/s?
Ans:{110 m/s}

(B) How far North is the car from the starting point after it accelerates for 75.0 s?
Ans:{11.6 km}

(C) At what angle (relative to due East) does the car have to head from its position after it accelerates for 75.0 s in order to head directly towards the starting point, the origin?
Ans:{-69.3^o}

(A) What are the SI units of a and b?
Ans:{a -> m/s³, b -> m/s}

(B) What is the particles instantaneous speed and direction (right or left) at t = 1.70 seconds?
Ans:{88.4 cm/s, right}

(D) What is the particle's instantaneous acceleration and direction at 1.70 seconds?
Ans:{46.4 cm/s², right}

(A) What is the horizontal velocity of the ball when it hits the wall?
Ans:{11.5 m/s}

(B) What is the initial velocity v_o with which the ball is launched?
Ans:{14.6 m/s}

(C) How high up the wall does the ball collided with the wall?
Ans:{3.44 m}

4. A car is moving around a circular track with a radius of 75.0 m at a constant speed. The car is observed to take 30.0 seconds to lap the track once.

(A) Determine the magnitude of the car’s velocity?
Ans:{15.7 m/s}

(B) After the car has gone 1/3 of the way around the track relative to due East, what are the x and y components of the car’s velocity?
Ans:{v_x = -13.6 m/s, v_y = -7.85 m/s}

(C) What is magnitude and direction of the car’s acceleration when the car has traveled 1/4 of the way around the track relative to due East?
Ans:{3.29 m/s², south)

Exam #2 2001

(A) Write down the equation for Newton Second Law in symbolic form for the pumpkin as a system.
Ans:{}

(B) Determine the mass of the pumpkin?
Ans{32.7 kg}

(C) How much energy is lost to friction when the pumpkin is pulled 2.40 m to the right?
Ans:{338 J}

2. A pumpkin of unknown mass is suspended by a cord and pushed away from vertical at an angle of 32.0^o when a 24.0 N force is applied to the pumpkin that makes an angle if 18.0^o with the horizontal.

(A) What is the tension in the cord?
Ans:{43.1 N}

(B) What is the mass in of the pumpkin?
Ans:{4.48 kg}

(C) What is the net force in the vertical direction on the pumpkin?
Ans:{43.9 N}

3. A 190 kg coffin is lifted at a constant speed of 3.80 m/s by a cord that is pulled by a garlic- powered motor with a constant power out put of 7.30 kilowatts. (A) What is the tension in the cord? Ans:{1860 N} (B) How much work does the motor do when the coffin has been lifted 2.90 meters above its starting position? Ans:{5.57 kW} (C) How much energy is lost by the system when the coffin reaches 2.90 m above its starting position? Ans:{171 J}

4. An 11.0 kg skull (mass A) hangs from the end of a cord that is connected to a 15.0 kg pumpkin (mass B) setting on a frictionless incline plane. If the pulley is frictionless and the tension in the cord is 27.0 N,

(A) What is acceleration of the pumpkin?
Ans:{7.35 m/s²}

(B) At what angle is the frictionless plane inclined?
Ans:{34.5^o}

(C) Write down Newton’s Second Law for the system of the pumpkin and the skull as one system and check your two answers above (in parts A & B) by placing them in this equation to see if the two sides of the Newton’s Law equation are equal.
Ans:{}

Exam #2 1999

(A) What is the net force on block A?
Ans:{112 N}

(B) What is the acceleration of either block?
Ans:{5.34 m/s }

(C) What is the magnitude of the force F _B acting on block B?
Ans:{246 N}

2. Two cords suspend a 39.0 kg block A equally. An 18.0 kg plate is suspended equally by two other cords connected to the block that each makes an angle of 24.0o with the bottom of the block. Finally a 4.70 kg bob is hung from the bottom of the plate. (A) What is the net force on the middle plate? Ans:{0} (B) What is the tension in either cord B? Ans:{273 N} (C) If cord C were cut, what would be the tension in either cord A? Ans:{279 N}

3. A 34.0 kg block A rest on frictionless plane inclined at 19.0o. Block A is connected to a 22.0 kg block B by a cord that runs through a frictionless pulley. If the system is released from rest , (A) What is the direction and magnitude of the acceleration of either block? Ans:{1.91 m/s2, right} (B) What is the net force acting on block A? Ans:{65.0 N} (C) What is the tension in the cord connecting the two blocks? Ans:{174 N}

4. A spring with a rest length of 21.0 cm and a spring constant of 4780 N/m is connected block A. Block A and B both rest on a horizontal surface with a coefficient of kinetic friction equal to .480. Block A (mass of 6.70 kg) is in contact with block B (mass of 13.0 kg). Both blocks are pushed to the left so that the spring is compressed to 18.0 cm in length and then released.

(A) What is the acceleration of either block when they are released?
Ans:{2.58 m/s²}

(B) What is the net force acting on block A?
Ans:{17.3 N}

(C) What force does block A exert on block B?
Ans:{94.6 N}

Exam #3 2001

(A) What is the mechanical energy of the block when it is half way up the ramp?
Ans:{177 J}

(B) What is the impulse does the block impart to the spring in compressing the spring 11.0 cm?
Ans:{24.3 kg m/s}

(C) What is the value of the spring constant k?
Ans:{23,200 N/m or 232 N/cm}

2. An 144 gram block A slides along a frictionless, horizontal surface to the right at an unknown speed. A133 gram block B slides to the left towards block A at the same speed as block A. The total initial kinetic energy of both blocks before they collide is 3.80 kJ and the two blocks stick together after they collide.

(A) What is the magnitude of initial velocity of the two blocks before they collide?
Ans:{166 m/s}

(B) What is the final velocity of the two blocks after they collide?
Ans:{6.58 m/s}

(C) What is the magnitude of the impulse that block A exerts on block B during the collision?
Ans:{22.9 N s}

3. Two pucks slide on a horizontal frictionless surface towards each other, collide and stick together and go off at 7.50 cm/s at an unknown angle q . Initially, puck A has a mass of 90.0 kg and is moving to the right. Initially, puck B has a mass of 28.0 kg and is moving at 55.0 cm/s at an angle of 32.0^o as shown.

(A) What is the momentum of the two blocks in the y-direction after they collide and stick together?
Ans:{8.16 N s}

(B) At what angle do the two pucks move off together?
Ans:{67.2^o}

(C) What is the initial speed of puck A?
Ans:{18.3 cm/s}

4. A 145 g baseball moving horizontally at 33.0 m/s is struck by a bat imparting a velocity of 48.0 m/s in the opposite direction at an angle of 49.0^o above horizontal. The ball is contact with the bat for 2.60 ms. (The acceleration is not constant so do not solve this problem using Newton’s second law and the constant acceleration kinematic equations or I will not count it.)

(A) What is the vertical impulse that the bat exerts on the ball?
Ans:{5.25 N s}

(B) What is the average horizontal force exerted by the bat on the ball?
Ans:{3600N}

(C) How much work does the bat do on the baseball if all of the work done by the bat went into the motion of the ball?
Ans:{88.1 J}

Exam #3 1999

(A) What is the magnitude of block A’s momentum just before it collides with block?
Ans:{30.0 kg m/s}

(B) What is the magnitude and direction of the velocity of block A after they collide?
Ans:{-2.29 m/s, left}

(C) What is the coefficient of restitution of the collision?
Ans:{0.735}

2. A 80 kg person and a 250 kg crate are sliding together across a frictionless lake at a speed of 99.0 cm/s to the left. The crate is ahead of the person. The person pushes against the crate in such a way that the person comes to a halt relative the surface of the lake.

(A) What impulse did the person exert on the crate to stop their motion?
Ans:{79.2 N S}

(B) What is the speed of the crate after they separate?
Ans:{1.31 m/s}

(C) How work did the person do on themselves and the crate during the “push”?
Ans:{51.7 J}

(A) What is the velocity of the center of mass of this system?
Ans:{25.8 cm/s}

(B) What is the initial speed v_o of the two blocks?
Ans:{43.3 cm/s}

(C) How long did the collision last?
Ans:{1.57 ms}

4. A 530 gram lump of putty A is moving at 29.0 m/s on a horizontal frictionless surface at an angle of 38.0^o relative to due east. It collides with another lump of putty B with a mass of 280 grams that is moving due west at 11.0 m/s. If the two lumps stick together after the collision,

(A) What is the magnitude and direction of the total momentum of the two lumps of putty before they collide ?
Ans:{13.1 kg m/s, 46.3^o}

(B) What is the speed and direction of the two lumps after the collision?
Ans:{16.1 m/s, 46.3^o}

(C) How many joules of energy were lost during the collision?
Ans:{134 J}

Exam #4 2001

(A) What is the angular deceleration of the ball?
Ans:{-4.76x10^-3 rad/s²}

(B) What is the frictional torque acting to slow the ball down?
Ans:{5.53x10^-5 N m}

(C) How much energy is lost to friction while the ball slows down to a stop?
Ans:{37.7 mJ}

2. An 16.0 kg bar that is 4.80 m long is suspended by a frictionless pivot that is 150 cm from its right end.

(A) What is the moment of inertia of the rod about its suspension point?
Ans:{43.7 kg m²}

(B) If the bar is held horizontally and released, what is the rod's initial angular acceleration?
Ans:{3.23 rad/s²}

(C) What is the angular velocity of the bar at the moment it is vertical if no energy is lost during its swing down?
Ans:{2.54 rad/s}

3. A 3.20 m long bar with a mass of 1.90 kg has a 840 gram pellet of negligible size attached to it center. The bar is rotating horizontally once every 1.40 seconds. Assume it is rotating on a frictionless surface so that gravitational effects can be neglected.

(A) How much energy did it take to set the bar and pellet into rotation?
Ans:{87.0 J}

(B) What force would the bar have to exert on the pellet to keep it from sidling outwards along the bar? Ans:{27.1 N}

(C) If the pellet is allowed to slide to the stop at the end of the bar, what would be the bar's angular velocity when the pellet is at the end of the bar?
Ans:{2.57 rad/s}

4. A sanding disk with a rotational inertia of 1.30x10^-3 kg·m² is attached to an electric drill whose motor delivers a constant torque of 16.0 N·m.

(A) Determine the angular velocity 32.0 ms after the motor is switched on. Ans:{394 rad/s}

(B) Determine the angular momentum of the sanding disk when the disk has made 980 revolution after the motor is switched on?
Ans:{16.0 kg m²/s}

(C) Determine how long it will take for the disk to have a rotational energy 740 Joules.
Ans:{86.7 ms}

Final Exam 2001

1. Car A is moving North at 44.0 km/hr while car B is pointed West and initially at rest. At the moment that car A passes car B, car B accelerates West with an acceleration of 1.30 km/hr/sec. (A) At what angle q will car B observe car A after 3.90 minutes? Ans:{16.1o} (B) After car A passes car B, how long will it take until car A is three times as far from the origin as car B is from the origin? Ans:{22.6 s}

2. A 260 N force is applied to an 18.0 kg block resting on an incline plane inclined at 32.0^o. The force is applied parallel to the incline plane, and the coefficient of kinetic friction is .550.

(A) What is the acceleration of the block?
{Ans: 4.68 m/s²}

(B) At what distance d up the incline plane will the block have a kinetic energy of 125 J if it started from rest?
Ans:{1.48 m}

3. A 1.50 kg block A and a 3.80 kg block B rest on a frictionless surface. A massless spring with a spring constant of 370 N/m is compressed and placed between the two blocks. When the spring is released, block A is observed to move to the left with a speed of 71.0 cm/s.

(A) How much energy is stored in the compressed spring before it is released?
Ans:{.527 J}

(B) What is the initial force that the spring exerts on either block at the moment the spring is first released?
Ans:{19.8 N}

4. The equation of motion for the location of a 3.90 kg object moving in a straight line is given by x(t) = a t³ - b t where the constants are a = 1.70 m/s³, and b = 15.9 m/s.

(A) At what moment (after t > 0) will the object’s velocity be zero?
Ans:{1.77 s}

(B) How much work is done on the object in 2.50 seconds?
Ans:{4.66 J}

5. A 47.0 kg girl is revolving on the end of a 3.50 m long rope on a frictionless ice-surface in such a way that it takes her 22.0 seconds to make one complete revolution.

(A) What force does she have to exert to hold on to the rope initially?
Ans:{13.4 N}

(B) If she pulls herself towards the center of rotation, how fast will she be moving when she has moved .500 m closer to the center of rotation?
Ans:{1.17 m/s}

6. A ball is dropped from an unknown height above the ground. When the object is 11.0 m above the ground, it is observed to moving at 25.0 m/s. Neglecting air resistance, (A) How long will it take the ball to reach the ground from 11.0 meters? Ans:{.407 s} (B) From what height was the ball dropped originally? Ans:{42.9 m}

7. A 3.30 kg solid disk with a radius of 26.0 cm is mounted on a frictionless bearings at its center. A 2.10 kg ring with a radius of 11.0 cm is attached to the disk so that they are concentric. A rope is wrapped around the ring and pulled by a constant force of 15.0 N.

(A) What is the angular acceleration of the system?
Ans:{12.0 rad/s²}

(B) How long will it take the system to have a rotational energy of 560 Joules if it starts from rest?
Ans:{7.51 s}

Final Exam 1999

(A) how fast will the ball be moving when it strikes the ground?
Ans:{32.6 m/s}

(B) from what height was the ball dropped originally?
Ans:{47.9 m}

(C) what is the total mechanical energy of the ball 1.50 s after it is launched?
Ans:{133J}

2. A block 3.50 kg block is pushed up a rough incline plane by a constant force of 38.0 N. The incline plane is tilted at 31.0^o and the block starts from rest. When the block is 28.0 cm above ground level its speed is observed to be 2.10 m/s.

(A) How much work is done by the applied force?
Ans:{20.7 J}

(B) What is the total mechanical energy of the block (relative to ground level) when the block is 28.0 cm above the ground?
Ans:{17.3 J}

(C) How many joules of energy are lost to heat due to friction between the block and the incline plane when the block is 28.0 cm above the floor?
Ans:{3.34 J}}

3. A 19.0 kg mass, initially at rest, explodes into three pieces, all moving horizontally outwards. Piece A has a mass of 6.30 kg and goes East at 22.0 m/s. Piece B has a mass of 4.50 kg and goes south at speed of 34.0 m/s. The explosion lasts for .00370 seconds.

(A) What is the speed and direction of the third piece C?
Ans:{25.2 m/s, 132^o Nof E}

(B) How much energy is released during the explosion?
Ans:{6.72 kJ}

(C) During the explosion, what average force exerted on piece A?
Ans:{37,500 N}

4. The equation of motion for the position of a 180 gram object moving in a straight line is given by where the constant a has a magnitude of 1.80 and t_o = 1.70 seconds.

(A) What are the SI units of the constant a?
Ans:{ a = m/s³}

(B) What is the momentum of the object at t = 8.30 seconds?
Ans:{57.8 kg m/s}

(C) What is the net force and its direction on the object initially at t = 0 seconds?
Ans:{ 1.10 N, left}

5. A 7.90 kg solid wheel with a radius of 53.0 cm is pivoted 18.0 cm from its center on a frictionless pivot. Initially the wheel is released from rest horizontally, i.e. when the 18.0 cm cord between the center of the wheel and the pivot point is horizontal. (A) What is the moment of inertia of the wheel about its pivot point? Ans:{1.37 kg m2} (B) What is initial angular acceleration of the wheel about the pivot point? Ans:{10.2 rad/s} (C) If there is no energy loss, what angular velocity will the wheel have when its center of mass is at its lowest point? Ans:{4.52 rad/s}

6. A 560 gram block is connected by a cord to pole. The block is sliding on a horizontal frictionless surface with an initial speed of 5.60 m/s and its center of mass is 1.80 m from the pole initially. As the block slides around the pole, the cord wraps itself around the pole, getting shorter with each revolution. (A) What is the initial angular momentum of the revolving block? Ans:{5.64 kg m2/s} (B) What is the angular velocity of the block when the cord is 28.0 cm shorter? Ans:{4.36 rad/s} (C) What is the tension in the cord when the cord is 28.0 cm shorter? Ans:{16.2 N}