1. Work done by spring = 0.279 Joules
2. Work lost due to friction = 0.716 Joules
3. Speed of block when first hit spring = 0.680 m/s
1. Using Hooke's law, the potential energy stored in the spring is
E = 0.5kx^2
where
E = potential energy
k = spring constant
x = distance the spring is deformed.
Substitute the known values into the formula
E = 0.5 223 N/m (0.05 m)^2
E = 111.5 N/m 0.0025 m^2
E = 0.27875 Nm
E = 0.27875 (kg m)/s^2 m
E = 0.27875 (kg m^2)/s^2
E = 0.27875 J
Rounding to 3 significant figures gives 0.279 Joules.
2. The amount of force needed due to kinetic friction is
F = k * Fn
where
k = coefficient of friction
Fn = Normal force
The normal force is the mass of the object multiplied by the gravitational acceleration so,
4.3 kg * 9.8 m/s^2 = 42.14 (kg*m)/s^2
Now multiply by the coefficient of friction, getting
42.14 (kg*m)/s^2 * 0.340 = 14.3276 (kg*m)/s^2
= 14.3276 N
So we have 14.3276 N over a distance of 5 cm (0.05m), so
14.3276 N * 0.05 m = 0.71638 Nm = 0.71638 J
Rounding to 3 significant figures gives 0.716 Joules
3. The total work done on the block is the work used to compress the spring plus the work lost due to friction, so
0.279 J + 0.716 J = 0.995 J
Now the energy of a moving object is expressed as the following equation.
E = 0.5 M V^2
where
E = Energy
M = Mass
V = Velocity.
So setting energy equal to the amount used to stop the mass, we get
0.995 J = 0.5 M V^2
0.995 (kg*m^2)/s^2 = 0.5 M V^2
Substituting the known mass, getting
0.995 (kg*m^2)/s^2 = 0.5 4.3kg V^2
0.995 (kg*m^2)/s^2 = 2.15 kg V^2
And solve for V
0.995 (kg*m^2)/s^2 = 2.15 kg V^2
0.462790698 m^2/s^2 = V^2
0.680287217 m/s = V
And finally, round to 3 significant figures, getting 0.680 m/s
