A block of mass 2.62 kg is kept at rest as it compresses a horizontal massless spring(k = 141 N=m) by 15.3 cm. As the block is released, it travels 0.627 m on a rough hori-
zontal surface before stopping.
The acceleration of gravity is 9.8 m/s2 :Calculate the coe±cient of kinetic friction between surface and block.
Use the stored spring potneital energy to dtermine the kinetic energy at release. The kinetic energy KE is converted to work done against friction.
KE = Ffriction * X = M*g*(mu,k)*X
Solve for "mu,k", which is the kinetic friction coefficient
a mass of 10kg moves with a velocity of 4ms-2 find it kinetic energy
To find the coefficient of kinetic friction (μk), we can use the conservation of energy principle. We'll start by finding the spring potential energy, and then equate it to the work done against friction:
1. Calculate the spring potential energy (PE_spring):
PE_spring = (1/2)kx^2
Where k is the spring constant (141 N/m) and x is the compression of the spring (15.3 cm = 0.153 m).
PE_spring = (1/2) * 141 N/m * (0.153 m)^2
2. Next, we'll find the kinetic energy at release (KE_initial) using the principle of conservation of energy:
PE_spring = KE_initial
KE_initial = PE_spring
KE_initial = (1/2) * 141 N/m * (0.153 m)^2
3. Now, let's calculate the work done against friction (W_friction). We know that the work done against friction is equal to the change in kinetic energy (KE_initial - KE_final). Since the block comes to a stop, the final kinetic energy (KE_final) is zero.
W_friction = KE_initial - KE_final
W_friction = KE_initial - 0
W_friction = KE_initial
4. Using the work-energy principle, we can express the work done against friction in terms of the frictional force (F_friction) and the distance traveled (X):
W_friction = F_friction * X
5. From the definition of kinetic friction, we know that F_friction = μk * M * g, where M is the mass of the block (2.62 kg) and g is the acceleration due to gravity (9.8 m/s²).
6. Equate the work done against friction to the expression involving frictional force and solve for μk:
KE_initial = F_friction * X
KE_initial = μk * M * g * X
μk = KE_initial / (M * g * X)
Substituting the given values:
μk = [(1/2) * 141 N/m * (0.153 m)^2] / (2.62 kg * 9.8 m/s² * 0.627 m)
Evaluating this expression will give you the coefficient of kinetic friction (μk).