Acceleration

Acceleration project

Purpose

Students will explore acceleration.

Theory

Acceleration happens any time the speed changes. This is its definition—a

time-change in speed: a = dv/dt. Zero

acceleration means the velocity is not changing. Thus it is possible for speed to be zero when acceleration is not (as when a rocket first starts its engines) and for acceleration to be zero when speed is not (as when an elevator is in steady motion).

An accelerometer is a device that detects acceleration. Modern versions use semiconductors in which electrical transmission depends on the internal stresses. Earlier varieties used simple springs, but there is a far easier way.

Procedure

1. Procure a water bottle and a piece of cord or string. Dental floss can be used, as can a thread pulled from aging cloth. It needs to be four inches or so.
2. Attach a small weight to the end of the string. It can be a bit of twig or a ball of aluminum foil, but it must float in water when the time comes for that.
3. The label needs to be peeled off the bottle because the weight will hang in it and needs to be visible. The easiest way to hang the weight in the bottle is simply to screw the cap on, trapping the thread against the rim.
4. Set the bottle upright on a tabletop or a smooth floor and give it a minute for the hanging weight to stop moving.

Now push the bottle suddenly to away and observe the weight. It responds to the acceleration-in fact its horizontal displacement is pretty much linearly proportional to the acceleration, but note the direction.

5. It should be possible to move the bottle forward at a steady speed along the floor or table (or just carry it) so the weight doesn’t move appreciably.

Quickly stop it and observe the motion of the weight. This event is a negative acceleration—a deceleration.

6. Fill the bottle with water with the weight still in there. Screw the cap on to trap the string again. Turn the bottle upside-down do the weight floats in the middle. Repeat steps 4 and 5.

Analysis

From the outside perspective, the weight swings backward if the bottle accelerates forward because the bottle is trying to leave the weight behind.

From the viewpoint of the bottle, there is an “acceleration force” like the one seeming to push people back in their seats when a car accelerates.

Please answer each of the following in Canvas using complete sentences:

1. When the bottle moved at a steady speed, what was its acceleration?
2. If the bottle is left to sit, the weight grows still, but the surface of the earth is going east at 1000 MPH. Why doesn’t the accelerometer respond to this?
3. Suppose the bottle were hung from the ceiling in a car and the car sped up.

The bottle would swing back in the car.

What would the weight do within the bottle (no water, just air)? Why?

4. Did the weight do something weird when the bottle was accelerated while full of water? What did it do? Why?

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PROBLEM SET 3: Kinematics

1. A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. You can ignore air resistance.

1. Where on the ground (relative to the position of the helicopter when she drops) should the stuntwoman have placed the foam mats that break her fall?
2. Draw x-t, y-t, Vx-t, and vy-t graphs of her motion.

2. A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D.

The hose shoots the water at 45° above the horizontal from the same level as the base of the tank and is a distance 6D away (see figure). For what range of launch speeds (vo) will the water enter the tank? Ignore air resistance, and express your answer in terms of D and g.

3. If7 = bt? + ct3j, where b and c are positive constants, when does the velocity vector

make an angle of 45.0° with the x- and y-axes?

4. The earth has a radius of 6380 km and turns around once on its axis in 24 h.

1. What is the radial acceleration of an object at the earth’s equator? Give your answer in m/s and as a fraction of g.
2. If arad at the equator is greater than g, objects will fly off the earth’s surface and into space. (We will see the reason for this in Chapter 5.) What would the period of the earth’s rotation have to be for this to occur?

5. According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy “Dizzy” Carlyle in a minor league game. The ball traveled 188 m (618 ft) before landing on the ground outside the ballpark.

1. Assuming the ball’s initial velocity was in a direction 45° above the horizontal and ignoring air resistance, what did the initial speed of the ball need to be to produce such a home run if the ball was hit at a point 0.9 m (3.0 ft) above ground level? Assume that the ground was perfectly flat.
2. How far would the ball be above a fence 3.0 m (10 ft) high if the fence was 116 m (380 ft) from home plate?