Conservation of Energy Experiment

Name:______Date:______
Mid-Year Review for Physics Honors (12-13)

Solve these problems on separate sheets of paper. This review will be worth 15% of your grade on the Mid-year Assessment, and must be handed in on the day of the test during the testing block. I will not accept any late submissions of this review. You may use a 3 by 5 inch note-card of formulas during your test.

Chapter 2. Motion in One Dimension:

1.  Nathan accelerates his skate board uniformly along a straight path from rest to 12.5 m/s in 2.5 s. Find Nathan’s displacement and acceleration during this time. (5.0 m/s2, 16.0 m)

2.  A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the instantaneous velocity at 1.00s, 3.00s, 4.50s, 7.50s. ( 5m/s, -2.5m/s, 0 m/s, 5 m/s)

3.  A toy train moves in a straight line. A velocity vs. time graph for the train is shown below.

a.  Describe the motion of the train between 12s and 15 s.

b.  Find the acceleration of the train for this time interval. (-4m/s2)

c.  What is the total displacement of the train? (-12 m)

4.  A ball is thrown vertically upward with a speed of 25 m/s from a height of 2.0 m.

a.  How long does it take the ball to reach the ground?(5.13s)

b.  How fast is the ball moving when it reaches the ground?(-25.27m/s)

c.  How high does the ball rise above the ground?(31.9m )

5.  A model rocket is launched straight upward with an initial speed of 60.0 m/s. It accelerates with a constant upward acceleration of 1.00 m/s2 until its engines stop at an altitude of 170 m.

(a)  What is the maximum height reached by the rocket? (371 m)

(b)  How long is the rocket in the air?(17.9 s)

6.  A ranger in a national park is driving at 56.0 km/h when a deer jumps into the road 65 ahead of the vehicle. After a reaction time t, the ranger applies the brakes to produce an acceleration of a = -3.00 m/s2. What is the maximum reaction time allowed if she is to avoid hitting the deer?(1.6 s)

Chapter 3. Two-dimensional Motion, Vectors and Projectiles:

7.  A jet airliner moving initially at 300 mi/h due east enters a region where the wind is blowing at 85 mi/h in a direction 27.5° north of east. What is the new velocity of the aircraft relative to the ground?

(377 mi/h @5.970 N of E)

8.  A river flows due east at 1.10 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 8.0 m/s due north relative to the water.

(a) What is the velocity of the boat relative to shore?(8.1m/s @82.20 N of E)
(b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?(41.2 m)
(c) If the boat wants to travel directly across, in what direction should it be rowed? (7.90 W of N)

9.  A rock is thrown horizontally from a 100m high cliff. It strikes level ground 90m from the base of the cliff. At what speed was it thrown? (19.9m/s)

10.  A scared kangaroo once cleared a fence by jumping with a speed of 8.42m/s at an angle of 55.2˚ with respect to the ground.

a. If the jump lasted 1.4s, how high was the fence? (2.4m)

b. What was the kangaroo’s horizontal displacement? (6.7m)

11.  A projectile is shot from the edge of a 140m high cliff with an initial speed of 100m/s at 37˚ above the horizontal.

a. What is the maximum height reached by the projectile? (324.9m)

b. How long is the projectile in the air? (14.3s)

c. How far from the base of the cliff does the projectile land? (1140m)

Chapter 4. Newton’s Laws and Forces:

12.  A 50kg Rita’s Ice sign is hanging from three ropes as represented in the diagram below. Determine the force exerted by the second and third ropes. (F3 = 522.1N, 154.4N)

13.  A 383N box is being pushed along a level floor by a 120N force at an angle of 40˚ above the horizontal. The coefficient of kinetic friction between the box and the floor is 0.16. What is the acceleration of the crate? (1.1 m/s2)

14.  Carl begins at rest on the top of a hill. He rollerblades down the hill, which has an incline of 20˚. He accelerates uniformly moving 30m in 5s.

a. What is Carl’s acceleration? (2.4m/s2)

b. What is the coefficient of kinetic friction between the rollerblades and the ground? (0.103)

c. What is Carl’s speed at the end of the 30m? (12m/s)

15.  A 75kg crate is uniformly accelerated up an incline of angle 25 degrees with the horizontal.

a.  The crate starts at rest and moves 7.00m up the incline in 1.2 seconds. Calculate the acceleration of the crate. (9.72 m/s2 )

b.  If the coefficient of sliding friction between the crate and the incline is 0.30, how much force is required to accelerate the crate up the incline? (1240 N)

Chapter 5. Work and Energy:

16.  A 66 kg diver steps off a 12 m tower and drops from rest straight down into the water. If he comes to rest 4.7 m beneath the surface, determine the average resistance force exerted on him by the water.

( 2300 N)

17.  Starting from rest, a 6.0-kg block slides 3.00 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is µk = 0.436.

(a) Determine the work done by the force of gravity. (88.2J)
(b) Determine the work done by the friction force between block and incline. (-66.6 J )
(c) Determine the work done by the normal force. (0 J)

18.  A light horizontal spring has a spring constant of 105 N/m. A 2.00 kg block is pressed against one end of the spring, compressing the spring by 0.100m. After the block is released, it travels 0.250 m before it comes to a stop. Find the coefficient of friction between the horizontal surface and the block. (0.107)

19. 

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
22

Chapter 7. Circular Motion and Gravity

20.  A 55.6 kg ice skater is moving at 3.98 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.796 m around the pole.

(a) Determine the force exerted by the horizontal rope on her arms.( 1110 N)
1(b) What is the ratio of this force to her weight?( 2.03)

21.  A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 35.5 m/s. With what maximum speed can it go around a curve having a radius of 71.5 m? (24.5 m/s)

22.  An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. She does so by banking the road in such a way that the force of the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path.

(a) Show that for a given speed of v and a radius of r, the curve must be banked at the angle θ such that tan θ = v2/rg.

(b) Find the angle at which the curve should be banked if a typical car rounds it at a 50.0 m radius and a speed of 14.0 m/s. (21.8 o)

23.  Tarzan (m = 67 kg) tries to cross a river by swinging from a 10 m long vine. His speed at the bottom of the swing (as he just clears the water) is 7.9 m/s. Tarzan doesn't know that the vine has a breaking strength of 1000 N. Does he make it safely across the river? Give the tension in the vine at the bottom of his swing to support your answer. (No, 1070N )

24.  A roller-coaster vehicle has a mass of 499 kg when fully loaded with passengers.

a) If the vehicle has a speed of 22.0 m/s at point A, what is the force of the track on the vehicle at

this point? (29000 N)
1((( b) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the

track? (12.1 m/s)

25.  Two objects attract each other with a gravitational force of magnitude 0.94 10-8 N when separated
by 20.0 cm. If the total mass of the objects is 5.03 kg, what is the mass of each? (3.34 kg, 1.69 kg)

26.  A satellite is in a circular orbit about the Earth at a height above the Earth equal to the Earth's mean radius.

(a) Find the satellite's orbital speed. (5580 m/s)1
(b) Find the period of its revolution. (4 hr)
2(c) Find the gravitational force acting on it. (1260N)
3

2(21
2

1