A block of mass 0.40 kg slides in a straight line with a constant speed of 0.30 m s–1 along a horizontal surface, as shown in Fig. 3.1.
Fig. 3.1
Assume that there are no resistive forces opposing the motion of the block.
The block hits a spring and decelerates. The speed of the block becomes zero when the compression of the spring is 8.0 cm.
(i)
Calculate the initial kinetic energy of the block.
kinetic energy = ....................................................... J [2]
(ii)
The variation of the compression x of the spring with the force F applied to the spring is shown in Fig. 3.2.
Fig. 3.2
Assume that the elastic potential energy of the spring when its compression is 8.0 cm is equal to the initial kinetic energy of the block.
Use your answer in (b)(i) to calculate the maximum force Fmax exerted on the spring by the block.
Fmax = ...................................................... N [2]
(iii)
Calculate the maximum deceleration of the block.
deceleration = ................................................. m s–2 [2]
(iv)
State and explain whether the block is in equilibrium:
• before it hits the spring
...........................................................................................................................................
• when its speed becomes zero.
...........................................................................................................................................
[2]
(v)
The block is now replaced by another block of the same mass. Frictional forces affect the motion of this block so that it has a speed of 0.25 m s–1 when it makes contact with the spring.
A short time later, the block has a speed of 0.15 m s–1 as it loses contact with the spring and moves back along its original path.
Calculate the magnitude of the change in momentum of the block.
change in momentum = .................................................... N s [2]