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**that for the stronger force.**

A constant force is exerted on a cart that is initially at rest on an air track. Friction between the cart and the track is negligible. The force acts for a short time interval and gives the cart a certain final speed. To reach the same final speed with a force that is only half as big, the force must be exerted on the cart for a time interval 1. four times as long as 2. twice as long as 3. equal to 4. half as long as 5. a quarter of that for the stronger force. Answer: 2.The final speed is proportional to the acceleration of the cart and the time over which it acts. Half the Force corresponds to half the acceleration, which requires twice the time to reach the same final velocity.

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**that of the lighter cart.**

A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. The same force is exerted for the same length of time on another cart, also initially at rest, that has twice the mass of the first one. The final speed of the heavier cart is 1. one-fourth 2. four times 3. half 4. double 5. the same as that of the lighter cart. Answer: 3.The final speed is proportional to both the force on the cart and the time over which it acts, and inversely proportional to the mass of the cart. Same force on twice the mass corresponds to half the acceleration. To reach the same final speed requires twice the time.

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**1. is equal to two times its initial speed. **

A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the cart is already moving with constant speed in the direction of the force at the moment we begin to apply the force. After we exert the same constant force for the same short time interval, the increase in the cart’s speed 1. is equal to two times its initial speed. 2. is equal to the square of its initial speed. 3. is equal to four times its initial speed. 4. is the same as when it started from rest. 5. cannot be determined from the information provided. Same acceleration over the same time interval corresponds to the same change in speed. Answer: 4.The increase in speed is proportional to both the force on the cart and the time over which it acts.

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**the downward weight W of the person.**

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical to 3. smaller than the downward weight W of the person. Answer: 1. In order for the person to be accelerated upward, the normal force exerted by the elevator floor on her must exceed her weight.

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**1. No—its speed is constant. 2. Yes. **

A car rounds a curve while maintaining a constant speed. Is there a net force on the car as it rounds the curve? 1. No—its speed is constant. 2. Yes. 3. It depends on the sharpness of the curve and the speed of the car. Answer: 2.Acceleration is a change in the speed and/or direction of an object. Thus, because its direction has changed, the car has accelerated and a force must have been exerted on it.

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In the 17th century, Otto von Güricke, a physicist in Magdeburg, fitted two hollow bronze hemispheres together and removed the air from the resulting sphere with a pump. Two eight-horse teams could not pull the halves apart even though the hemispheres fell apart when air was readmitted. Suppose von Güricke had tied both teams of horses to one side and bolted the other side to a heavy tree trunk. In this case, the tension on the hemispheres would be 1. twice 2. exactly the same as 3. half what it was before. Answer: 1. If both teams pull on the hemispheres from one side with twice the force and the hemispheres remain at rest because the other side is bolted to a tree trunk, the tree must exert an equal and opposite force. Thus, the tension is doubled.

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**Consider a horse pulling a buggy. Is the following statement true?**

The weight of the horse and the normal force exerted by the ground on the horse constitute an interaction pair that are always equal and opposite according to Newton’s third law. 1. yes 2. no They are not always equal, on an incline for example. Answer: 2. The normal force is a repulsive contact force between the ground and the horse. The weight is the gravitational force exerted by Earth on the horse. These two forces are of different origin and do not constitute an interaction pair. The normal force is a repulsive contact force between the ground and the horse. The weight is the gravitational force exerted by Earth on the horse. These two forces are of different origin and do not constitute an interaction pair.

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**1. the two forces form an interaction pair. **

Consider a car at rest. We can conclude that the downward gravitational pull of Earth on the car and the upward contact force of Earth on it are equal and opposite because 1. the two forces form an interaction pair. 2. the net force on the car is zero. 3. neither of the above Answer: 2.These two forces cannot be an interaction pair because they act on the same object. Because the car is at rest, however, its momentum is constant (and zero). Because net force equals the time rate of change in momentum, the net force on the car must be zero. This means that the two forces must be equal and opposite. Choice 1 is not true because both forces act on the same object!

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The setup photographed below, known as a horizontal Atwood machine, consists of a heavy cart connected by a string passing over a pulley to a lighter mass. In this case the mass of the cart M = 875 grams and the mass hanging on the end of the string m = 200 grams. When the system is held in place the spring scale indicates that the force (in grams) pulling on the cart is equal to the mass m hanging on the string, as seen in the lower photograph. Assume that because this is physics the pulley is frictionless. After the system is released and begins to move the spring scale will read: (1) 0 grams. (2) greater than 0 but less than 200. (3) 200 grams. (4) greater than 200 grams.

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