A block is pulled horizontally across the rough surface of a table by means of a spring scale at constant speed. The reading on the spring scale is 14N .the pulling force is now increased to 31N and the block experiences an acceleration of 8,5m's squared calculate the friction between the block and the table surface
block mass = m
weight = m g
normal force on surface = m g
friction force = mu m g = 14N given so mu = 14/mg
31 - 14 = m a
17 = m a = 8.5 m given
so m = 17/8.5 = 2
mu = 14/2g = 14 /[2 g]
= 14 / 20
if g = 10 then mu = 0.7
14-Ff = M*a.
14-Ff = M*0 = 0,
Ff = 14N. = force of friction.
To calculate the friction between the block and the table surface, we can first determine the net force acting on the block.
1. First, we need to find the initial net force when the block is pulled with a constant speed. At constant speed, the net force is zero.
2. So, when the reading on the spring scale is 14N, the force of friction opposing the pulling force is also 14N.
3. Now, let's calculate the net force when the pulling force is increased to 31N and the block experiences an acceleration of 8.5 m/s^2.
Net force (F_net) = ma
F_net = (mass of the block) * (acceleration)
We need to find the mass of the block. To do that, we can use the initial net force of 14N.
F_net = friction force
F_net = friction force = mass of the block * acceleration due to gravity
Therefore, the mass of the block = (friction force) / (acceleration due to gravity)
Acceleration due to gravity, g = 9.8 m/s^2
4. Calculate the mass of the block:
mass of the block = 14N / 9.8 m/s^2
5. Now that we have the mass of the block, we can calculate the net force at 31N using the same formula:
F_net = (mass of the block) * (acceleration)
31N - (friction force) = (mass of the block) * (8.5 m/s^2)
6. Substitute the mass of the block from step 4 and solve for the friction force:
31N - friction force = ((14N / 9.8 m/s^2) * (8.5 m/s^2))
31N - friction force = 12.0408 kg*m/s^2
friction force = 31N - 12.0408 kg*m/s^2
Therefore, the friction between the block and the table surface is approximately 18.96N.
To calculate the friction between the block and the table surface, we can use Newton's second law of motion.
First, let's determine the net force acting on the block. We know that the force applied by the spring scale is the pulling force and is equal to 31 N. The weight force acting on the block can be calculated using the equation:
Weight = mass * gravitational acceleration
Assuming the gravitational acceleration is 9.8 m/s^2 and the mass of the block is unknown, we can use the relationship between weight and mass to rewrite the equation as:
Weight = mass * 9.8 m/s^2
Next, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = mass * acceleration
Since there is an acceleration of 8.5 m/s^2, we can substitute the given values:
Net force = mass * 8.5 m/s^2
Let's denote the frictional force as F_friction. Since the block is moving at a constant speed, the frictional force is equal to the applied force (31 N), resulting in no net force:
F_friction = 31 N
However, when the block experiences an acceleration, the net force is no longer zero. The net force acting on the block is the difference between the applied force and the frictional force:
Net force = Applied force - Frictional force
Substituting the given values:
mass * 8.5 m/s^2 = 31 N - F_friction
Now, to find the mass of the block, we need to rearrange the equation:
mass = (31 N - F_friction) / 8.5 m/s^2
To further solve for F_friction, we need to determine the mass of the block. This can be done by substituting the mass value into the previously calculated equation for weight:
Weight = mass * 9.8 m/s^2
Solving for mass:
mass = Weight / 9.8 m/s^2
Now, we can substitute the given values for weight and solve for the mass of the block.
Once we have the mass of the block, we can substitute it back into the equation for F_friction to calculate the frictional force.