Download Work-Energy Practice

Work-Energy Practice
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1. The force acting on a particle varies as in the Figure below (The x axis is marked in increments of 5.00 m.)
Find the work done by the force as the particle moves across the following distance from x = 0 m to x = 60.0 m.
(90 J)
2. A 2.5 kg object is subject to a force Fx that varies with position as in the Figure below. What is the total work
done by the force over the distance x = 0 to x = 15.0 m? If the object starts from rest, what is its final
velocity?(30 J, 4.9 m/s)
3. A 3.0 m long pendulum is released from rest when the support string is at an angle of 28° with the vertical.
What is the speed of the bob at the bottom of the swing?(2.62 m/s)
4. An archer pulls her bow string back 0.430 m by exerting a force that increases uniformly from zero to 235 N.
(a) What is the equivalent spring constant of the bow?( 547 N/m)
(b) How much work does the archer do in pulling the bow?(50.5 J)
5. A block of mass 12.0 kg slides from rest down a frictionless 38.0° incline and is stopped by a strong spring
with k = 3.50 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest
against the spring. When the block comes to rest, how far has the spring been compressed?(0.111 m)
6. (a)A 80 kg man steps out a window and falls (from rest) 1.3 m to a sidewalk. What is his speed just before his
feet strike the pavement? (5.05 m/s)
(b) If the man falls with his knees and ankles locked, the only cushion for his fall is an approximately 0.47 cm
give in the pads of his feet. Calculate the average force exerted on him by the ground in this situation. This
average force is sufficient to cause cartilage damage in the joints or to break bones.(2.18X105 N)
7. A toy gun uses a spring to project a 6.0 g soft rubber sphere horizontally. The spring constant is 12.0 N/m,
the barrel of the gun is 13.8 cm long, and a constant frictional force of 0.032 N exists between barrel and
projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.2 cm for this
launch?(1.98 m/s)
8. An 83.0 N box is pulled 24.0 m up a 30° incline by an applied force of 101 N that points upward, parallel to
the incline. If the coefficient of kinetic friction between box and incline is 0.220, calculate the change in the
kinetic energy of the box. (1050 J)
9. A ski jumper starts from rest 55.0 m above the ground on a frictionless track and flies off the track at an angle
of 45.0° above the horizontal and at a height of 19.0 m above the ground. Neglect air resistance.
(a) What is her speed when she leaves the track? (26.6 m/s)
(b) What is the maximum altitude she attains after leaving the track? (37 m)
(c) Where does she land relative to the end of the track?(87.6 m)
10. The electric motor of a model train accelerates the train from rest to 0.685 m/s in 17.0 ms. The total mass of
the train is 875 g. Find the average power delivered to the train during its acceleration.( 12.1 W)
11. A 1.50 103 kg car starts from rest and accelerates uniformly to 19.8 m/s in 11.2 s. Assume that air
resistance remains constant at 400 N during this time.
(a) Find the average power developed by the engine. (30200 W)
(b) Find the instantaneous power output of the engine at t = 11.2 s, just before the car stops accelerating.
(60400 W)
12. A 1.700 kg bead slides on a curved wire, starting from rest at point A in Figure P5.28. If the wire is
frictionless, find each of the following.
(a) the speed of the bead at B (9.9 m/s)
(b) the speed at C (7.67 m/s)
13. A projectile is launched with a speed of 40 m/s at an angle of 59° above the horizontal. Use conservation of
energy to find the maximum height reached by the projectile during its flight. (60 m)
14. A 0.250 kg block is placed on a light vertical spring (k = 4.80 103 N/m) and pushed downward,
compressing the spring 0.100 m. After the block is released, it leaves the spring and continues to travel upward.
What height above the point of release will the block reach if air resistance is negligible? (9.8 m)
15. A 74 kg diver steps off a 12 m tower and drops from rest straight down into the water. If he comes to rest
4.0 m beneath the surface, determine the average resistance force exerted on him by the water. (2900 N)
16. An airplane of mass 1.4 104 kg is moving at 58 m/s. The pilot then revs up the engine so that the forward
thrust by the air around the propeller becomes 7.0 104 N. If the force exerted by air resistance on the body of
the airplane has a magnitude of 5.0 104 N, find the speed of the airplane after it has traveled 500 m. Assume
that the airplane is in level flight throughout this motion. (69.2 m/s)
17. A 2.10 103 kg car starts from rest at the top of a 5.1 m long driveway that is inclined at 19° with the
horizontal. If an average friction force of 4.0 103 N impedes the motion, find the speed of the car at the bottom
of the driveway. (3.62 m/s)
18. A 29.0 kg child on a 3.00 m long swing is released from rest when the ropes of the swing make an angle of
32.0° with the vertical.
(a) Neglecting friction, find the child's speed at the lowest position.(2.99 m/s)
(b) If the speed of the child at the lowest position is 2.60 m/s, what is the mechanical energy lost due to friction?
(31.5 J)
19. In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 5.0 m/s up a
25.0° inclined track. The combined mass of monkey and sled is 22 kg, and the coefficient of kinetic friction
between sled and incline is 0.20. How far up the incline do the monkey and sled move? (2.11 m)
20. An 80.0 kg sky diver jumps out of a balloon at an altitude of 1160 m and opens the parachute at an altitude
of 200.0 m. Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed
and constant at 3600 N with the parachute open, what is the speed of the diver when he lands on the ground?
(59.5 m/s)
21. A stunt man whose mass is 70 kg swings from the end of a 4.1 m long rope along the arc of a vertical circle.
Assuming that he starts from rest when the rope is horizontal, find the tensions in the rope that are required to
make him follow his circular path at each of the following points.
(a) at the beginning of his motion (0 N)
(b) at a height of 1.5 m above the bottom of the circular arc (1310 N)
(c) at the bottom of the arc (2060 N)
22. Refer to the following information for the next four questions.
a. At what point along this frictionless wire, will a 100-gram bead released from rest at point A have the greatest speed?
b. How fast will the bead be traveling is it passes through points C and E? (4.43 m/s)
c. Consider a second scenario in which the wire exerts a constant frictional force of 0.3 N on the bead. If the bead has to slide 3 meters
along the wire in order to reach point C, will it make it to C? If yes, how fast would it be moving?(1.26 m/s)
d. Why did we not care about the length of the wire when it was frictionless?
23. A projectile is released at 15 m/sec at an angle of 37º from the top of a 30 meter balcony.
a. How fast will it be moving as it passes through the apex of its trajectory? (12 m/s)
b. How high will it rise above the ground? (34.13 m)
b. How fast will it be traveling when it strikes the ground? (28.51 m/s)
24. A 250-gram pendulum bob is initially constrained at a 53º angle by two strings as shown below.
a. When the horizontal string is cut the pendulum begins to swing. As the pendulum bob passes through its
equilibrium position, what will be its velocity? (2.8 m/s)
b. As the pendulum bob passes through its equilibrium position, what will be the tension in the supporting
string? (4.4 N)
Rollercoaster Practice:
ANSWERS: 1. 40.84 m/s, 2. 40.84 m/s, 3. 83.4 m/s2, 4. 9.51 g’s, 5.29.73 m/s, 6. 44.2 m/s2, 7. 3.5 g’s,
8. 31.34 m/s
ANSWERS: 1. 40.84 m/s, 2. 40.84 m/s, 3. 33.4 m/s2, 4. 4.4 g’s, 5. 29.73 m/s, 6. 88.4 m/s2,
7. 8.02 g’s, 8. 31.34 m/s
ROLLER COASTER DETECTIVE
1 What is the height, between "A" and "B?"
2 What is the centripetal acceleration at "B?"
3 What is the radius of the track at "B?"
4 How high is location "C?"
5 What is the radius of the track at location "C?"
6 What is the velocity of the car at location "D?"
ANSWERS
1 ) 39.54 m 2 ) 29.4 m/s2 3 ) 26.67 m 4 ) 35.87 m 5 ) 2.76 m 6 ) 19.80 m/s
ADVANCED SHEET
1 What is the height, between "B" and "C?"
2 What is the centripetal acceleration at "C?"
3 What is the radius of the track at "C?"
4 How high is location "D?"
5 What is the radius of the track at location "D?"
6 How fast is the car traveling at location "E?"
7 How far is the spring compressed from its hanging position, x?
8 If the car traveled up the first hill in 1.2 minutes, then how much power was used to pull it up the hill in
horsepower?
ANSWERS
1 ) 62.04 m 2 ) 29.4 m/s2 3 ) 41.7 m 4 ) 55.15 m 5 ) 7.34 m 6 ) 28.86 m/s 7 ) 5.89 m
8 ) 8.76 hp, 6533 w