FORCE, MASS AND ACCELERATION

Questions 1-2 refer to a toy car that can move in either direction along a horizontal line (the + position axis).

Assume that friction is so small that it can be ignored. A force toward the right of constant magnitude is applied to the car.

1. Sketch on the axes below using a solid line the shape of the car’s acceleration—time graph.

2. Suppose that the mass of the car were twice as large. The same constant force is applied to the car. Sketch on the axes above using a dashed line the car’s acceleration—time graph. Explain any differences in this graph compared to the car’s acceleration—time graph with the original mass.

3. When a force is applied to an object with mass equal to the standard kilogram, the acceleration of the mass is 3.25 m/s2. (Assume that friction is so small that it can be ignored.) When the same magnitude force is applied to another object, the acceleration is 2.75 m/s2. What is the mass of this object? What would the second object’s acceleration be if a force twice as large were applied to it? Show your calculations.

4. Given an object with mass equal to the standard kilogram, how would you determine if a force applied to it has magnitude equal to one newton? (Assume that frictional forces are so small that they can be ignored.)

In Question 5, assume that friction is so small that it can be ignored.

5. The spring scale in the diagram below reads 10.5 N. If the cart moves toward the right with an acceleration also toward the right of 3.25 m/s2, what is the mass of the cart? Show your calculations and explain.

In Questions 6 – 8, friction may not be ignored.

6. The force applied to the cart in Question 5 by spring scale F1 is still 10.5 N. The cart now moves toward the right with a constant velocity. What are the magnitude and direction of the frictional force? Show your calculations and explain your reasoning.

7. The force applied to the cart in Question 5 by spring scale F1 is still 10.5 N. The cart now moves toward the right with an acceleration also toward the right of 1.75 m/s2. What are the magnitude and direction of the frictional force? Show your calculations and explain.

8. The force applied to the cart by spring scale F1 is 10.5 N. The cart now moves toward the right with a constant velocity. The frictional force has the same magnitude as in Question 7. What does spring scale F2 read? Show your calculations and explain.