Worksheet Chapter 1: Force and Motion II

1. A spring system consists of two identical springs (each with spring constant k = 300 N m⁻¹) connected in parallel, suspended vertically from a rigid support. A third identical spring is attached in series below this parallel combination. (a) Find the effective spring constant k_eff of this composite system. (b) Calculate the total extension produced when a 45 N load is suspended from the bottom of the system.

2. Fill in the blank: The single force that represents the combined vector sum of two or more forces acting on an object is known as the ________ force.

3. A worker pulls a heavy crate of mass 40 kg across a concrete floor using a rope inclined at 35° above the horizontal with a tension force of 120 N. (a) Calculate the horizontal component of the pulling force. (b) Calculate the vertical component of the pulling force.

4. A spring has an original length of 15.0 cm. When a load of 6.0 N is hung from it, its extended length becomes 19.0 cm. (a) Determine the spring constant k in N cm⁻¹. (b) Calculate the length of the spring when a load of 10.0 N is hung from it (assuming elastic limit is not exceeded).

5. An object of weight 50 N is suspended in air by two strings. String A makes an angle of 45° with the horizontal ceiling and String B makes an angle of 45° with the horizontal ceiling. (a) Draw or describe the vector resolve equation for vertical forces. (b) Calculate the tension T in each string.

6. Which arrangement of two identical springs will result in a STIFFNESS (effective spring constant) that is GREATER than a single spring?

7. A car of mass 1200 kg is parked on a hill inclined at an angle of 15° to the horizontal. (a) Calculate the component of the car's weight acting parallel down the slope. (b) State the magnitude of the static friction force keeping the car stationary on the slope.

8. True or False: If three coplanar forces acting on a point are in equilibrium, they can be drawn as a closed triangle of forces in a head-to-tail sequence.

9. A wooden box of mass 12 kg sits on a smooth horizontal table. Two perpendicular horizontal forces of 15 N east and 20 N north are applied to the box. (a) Calculate the magnitude of the resultant force acting on the box. (b) Calculate the acceleration of the box.

10. True or False: When an object moves at a constant velocity, the resultant force acting on it is equal to zero.