Find the coefficient of kinetic friction between a 4.3- block and the horizontal surface on which it rests if an 80 spring must be stretched by 2.7 to pull the block with constant speed. Assume the spring pulls in a direction 13 above the horizontal.
without units, the numerals in your problem are absolutely meaningless.
My bad.
Find the coefficient of kinetic friction between a 4.3-kg block and the horizontal surface on which it rests if an 80 N/m spring must be stretched by 2.7 cm to pull the block with constant speed. Assume the spring pulls in a direction 13 degree above the horizontal.
ok,the force is kx or 80*.027 N
Now look at the components of force.
the vertical component reduces the normal force.
fn=mg-kx*sin13
so friction is mu*(mg-kx*sin13)
and friction force has to equal the horizontal component for the spring, kx*cos13
set them equal, and you have it.
thank you!
may God bless you Bob :)
To find the coefficient of kinetic friction between the block and the horizontal surface, we need to use the information given about the spring force and the block's motion.
Let's break down the problem step by step:
1. Start by identifying the relevant forces acting on the block. In this case, we have the force of gravity pulling the block downward and the spring force pulling the block horizontally.
2. Given that the spring must be stretched by 2.7 cm (which is equivalent to 0.027m), we can use Hooke's Law to determine the spring force. Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position.
F_spring = k * x
Where:
F_spring is the spring force (in Newtons),
k is the spring constant (in N/m), and
x is the displacement of the spring (in meters).
3. The force of gravity acting on the block can be calculated using the block's mass (4.3 kg) and the acceleration due to gravity (9.8 m/s^2).
F_gravity = m * g
Where:
F_gravity is the force of gravity (in Newtons),
m is the mass of the block (in kilograms), and
g is the acceleration due to gravity (9.8 m/s^2).
4. Since the block is being pulled at a constant speed, the net force acting on the block must be zero. This means that the force of gravity and the spring force must balance each other out.
F_gravity = F_spring
This is because if there was any unbalance, the block would have either an accelerating or decelerating motion.
5. Now, we can substitute the equations and solve for the spring constant (k):
m * g = k * x
k = (m * g) / x
Substitute the given values:
m = 4.3 kg
g = 9.8 m/s^2
x = 0.027 m
k = (4.3 kg * 9.8 m/s^2) / 0.027 m = 1569.63 N/m
6. Next, we need to find the horizontal component of the spring force, which would counteract the kinetic friction. To determine this component, we need to find the component of the spring force in the horizontal direction.
F_horizontal = F_spring * cos(13)
Substitute the known values:
F_spring = 1569.63 N (from step 5)
θ = 13 degrees
F_horizontal = 1569.63 N * cos(13) = 1526.47 N
7. The kinetic friction force can now be determined by multiplying the coefficient of kinetic friction (μ) by the normal force (N). The normal force is the force exerted by the surface perpendicular to the block's weight.
F_friction = μ * N
Since the block is not moving vertically, the normal force is equal to the weight of the block.
N = m * g = 4.3 kg * 9.8 m/s^2 = 42.14 N
Substitute the known values:
F_friction = 1526.47 N
1526.47 N = μ * 42.14 N
8. Finally, we can solve for the coefficient of kinetic friction (μ):
μ = F_friction / N
= 1526.47 N / 42.14 N
= 36.24