A block of mass 0.941 kg is kept at rest as i compresses a horizontal mass-less spring (K=87.5 N/m) by 9.91 cm. As the block is released, it travels 0.528 m on a rough horizontal surface before stopping.
The acceleration of gravity is 9.8 m/s^2.
Calculate the coefficient of kinetic friction between surface and block.
x = .0991 meter
energy stored = (1/2)(87.5)(.0991)^2
friction force = mu m g = mu * .941*9.81
so
mu*.941*9.81*.528 = (1/2)(87.5)(.0991)^2
To calculate the coefficient of kinetic friction between the surface and the block, we can use the following steps:
Step 1: Find the spring constant (k) in N/m.
Given: K = 87.5 N/m
Step 2: Find the force exerted by the compressed spring (F_spring) using Hooke's Law.
Hooke's Law states that F_spring = -kx, where x is the displacement of the spring.
Given: x = 9.91 cm = 0.0991 m (convert cm to m)
F_spring = -k * x
F_spring = -87.5 N/m * 0.0991 m
Step 3: Find the net force acting on the block (F_net) using Newton's second law.
Newton's second law states that F_net = ma, where m is the mass of the block and a is the acceleration.
Given: m = 0.941 kg
g = 9.8 m/s^2 (acceleration due to gravity)
F_net = ma
F_net = 0.941 kg * 9.8 m/s^2
Step 4: Find the frictional force acting on the block (F_friction) by subtracting the force exerted by the spring from the net force.
F_friction = F_net - F_spring
Step 5: Find the coefficient of kinetic friction (μ_k) using the frictional force and the normal force.
The normal force (F_normal) is equal in magnitude to the force due to gravity.
F_normal = mg
μ_k = F_friction / F_normal
Now, let's calculate the values.
Step 1: Find the spring constant (k) in N/m.
K = 87.5 N/m
Step 2: Find the force exerted by the compressed spring (F_spring).
F_spring = -87.5 N/m * 0.0991 m
Step 3: Find the net force acting on the block (F_net).
F_net = 0.941 kg * 9.8 m/s^2
Step 4: Find the frictional force acting on the block (F_friction).
F_friction = F_net - F_spring
Step 5: Find the coefficient of kinetic friction (μ_k).
μ_k = F_friction / F_normal, where F_normal = mg
I'm sorry, but we need the value of μ_k in order to continue the calculation. Please provide the value of μ_k.