Question

2. A block of mass m is placed against a spring with spring constant k, as shown in figure 1. The spring is compressed over a distance $x_0$, and then released. The spring expands until it reaches its equilibrium at x = 0, where the block leaves the spring and continues to slide to the right. The block slides over a frictionless surface. m $x_i = -x_0$ $x_f = 0$ Figure 1. M (a) Write down the equation for the work done by the elastic force in the spring as it expands from $x_i$ to $x_f$, and by using this equation show that the potential energy in the spring is: $U_s(x) = \frac{1}{2}kx^2$ Briefly explain why the potential energy of the spring increases for both positive and negative x. (4 marks) (b) Calculate the speed of the block as it leaves the spring at x = 0. (3 marks) (c) After a short time, the block collides with another block of mass M. Both blocks stick together and slide onwards. State what type of collision this is, and derive equations for (i) the speed of the blocks after the collision, and (ii) the energy lost in the collision. (3 marks)

          2.
A block of mass m is placed against a spring with spring constant k, as shown in figure 1. The
spring is compressed over a distance $x_0$, and then released. The spring expands until it
reaches its equilibrium at x = 0, where the block leaves the spring and continues to slide to the
right. The block slides over a frictionless surface.
m
$x_i = -x_0$
$x_f = 0$
Figure 1.
M
(a) Write down the equation for the work done by the elastic force in the spring as it
expands from $x_i$ to $x_f$, and by using this equation show that the potential energy in the
spring is:
$U_s(x) = \frac{1}{2}kx^2$
Briefly explain why the potential energy of the spring increases for both positive and
negative x.
(4 marks)
(b) Calculate the speed of the block as it leaves the spring at x = 0.
(3 marks)
(c) After a short time, the block collides with another block of mass M. Both blocks stick
together and slide onwards. State what type of collision this is, and derive equations for
(i) the speed of the blocks after the collision, and (ii) the energy lost in the collision.
(3 marks)

2.
A block of mass m is placed against a spring with spring constant k, as shown in figure 1. The
spring is compressed over a distance x0, and then released. The spring expands until it
reaches its equilibrium at x = 0, where the block leaves the spring and continues to slide to the
right. The block slides over a frictionless surface.
m
xi = -x0
xf = 0
Figure 1.
M
(a) Write down the equation for the work done by the elastic force in the spring as it
expands from xi to xf, and by using this equation show that the potential energy in the
spring is:
Us(x) = (1)/(2)kx^2
Briefly explain why the potential energy of the spring increases for both positive and
negative x.
(4 marks)
(b) Calculate the speed of the block as it leaves the spring at x = 0.
(3 marks)
(c) After a short time, the block collides with another block of mass M. Both blocks stick
together and slide onwards. State what type of collision this is, and derive equations for
(i) the speed of the blocks after the collision, and (ii) the energy lost in the collision.
(3 marks)

Added by Robert G.

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