A 2.0 kg block of iron slides along a floor, decreasing its speed from 4.0 m/s to 1.0 m/s.
a) How much work does the frictional resistance of the floor do on the block?
b) If the reduction in velocity occurred over a distance of 10 m, what was the force of
friction acting on the block?
c) What impulse was delivered to the block?
work = change in Ke
= (1/2)(2)(1^2-4^2) = -15 J
negative because energy taken out not put in
work = force * distance in direction of force
-15 = F (10)
F = -1.5 N
impulse = change in momentum
I = 2 ( 1 - 4) = -6 kg m/s
THANKS
a) To calculate the work done by friction, we can use the work-energy principle. The work done by a force can be calculated by multiplying the force by the distance over which the force is applied. In this case, the frictional force acts in the opposite direction of the motion, so it does negative work.
The work done by friction can be calculated as:
Work = Force × Distance × cos(180°)
The force of friction can be calculated using the equation:
Force of friction = mass × acceleration
The acceleration can be calculated using Newton's second law:
acceleration = (final velocity - initial velocity) / time
Since there is no given information about the time taken, we will assume that the block slows down uniformly, which means that the deceleration is constant.
Given:
Mass of the block (m) = 2.0 kg
Initial velocity (v₁) = 4.0 m/s
Final velocity (v₂) = 1.0 m/s
Distance (d) = 10 m
First, let's calculate the acceleration:
acceleration = (v₂ - v₁) / time
Since we don't have any info about time, we will proceed assuming it's uniformly decelerating.
acceleration = (1.0 m/s - 4.0 m/s) / t
acceleration = -3.0 m/s / t
Now let's calculate the force of friction:
Force of friction = mass × acceleration
Force of friction = 2.0 kg × (-3.0 m/s²) = -6.0 kg·m/s²
Finally, let's calculate the work done by friction:
Work = Force × Distance × cos(180°)
Work = (-6.0 kg·m/s²) × 10 m × cos(180°)
Work = -60 J
The frictional resistance of the floor does -60 Joules of work on the block.
b) The force of friction acting on the block can be calculated using the formula:
Force of friction = mass × acceleration
Using the same values as before:
Force of friction = 2.0 kg × (-3.0 m/s²) = -6.0 kg·m/s²
The force of friction acting on the block is -6.0 kg·m/s².
c) The impulse delivered to the block can be calculated using the equation:
Impulse = final momentum - initial momentum
The momentum of the block can be calculated using the equation:
Momentum = mass × velocity
Given:
Mass of the block (m) = 2.0 kg
Initial velocity (v₁) = 4.0 m/s
Final velocity (v₂) = 1.0 m/s
Initial momentum = mass × initial velocity
Initial momentum = 2.0 kg × 4.0 m/s = 8.0 kg·m/s
Final momentum = mass × final velocity
Final momentum = 2.0 kg × 1.0 m/s = 2.0 kg·m/s
Impulse = final momentum - initial momentum
Impulse = 2.0 kg·m/s - 8.0 kg·m/s = -6.0 kg·m/s
The impulse delivered to the block is -6.0 kg·m/s.
To answer these questions, we need to use the laws of motion and work-energy principles. Let's break them down one by one:
a) To calculate the work done by the frictional resistance of the floor, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (KE_initial) of the block is given by KE_initial = (1/2) * m * v_initial^2, where m is the mass of the block and v_initial is its initial velocity.
The final kinetic energy (KE_final) of the block is given by KE_final = (1/2) * m * v_final^2, where v_final is its final velocity.
The work done (W) by the frictional resistance is equal to the change in kinetic energy: W = KE_final - KE_initial.
Substituting the given values (m = 2.0 kg, v_initial = 4.0 m/s, and v_final = 1.0 m/s) into the equations, we can find the work done by the frictional resistance.
b) To calculate the force of friction acting on the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
The acceleration of the block can be determined using the formula: (v_final^2 - v_initial^2) / (2 * d), where d is the distance over which the reduction in velocity occurred.
The force of friction can be calculated using F_friction = m * a, where F_friction is the force of friction and m is the mass of the block.
Substituting the given values (m = 2.0 kg, v_initial = 4.0 m/s, v_final = 1.0 m/s, and d = 10 m) into the equations, we can find the force of friction acting on the block.
c) The impulse delivered to the block can be calculated using the impulse-momentum theorem, which states that the impulse on an object is equal to the change in its momentum.
The initial momentum (p_initial) of the block is given by p_initial = m * v_initial, where m is the mass of the block and v_initial is its initial velocity.
The final momentum (p_final) of the block is given by p_final = m * v_final, where v_final is its final velocity.
The impulse (J) delivered to the block is equal to the change in momentum: J = p_final - p_initial.
Substituting the given values (m = 2.0 kg, v_initial = 4.0 m/s, and v_final = 1.0 m/s) into the equations, we can find the impulse delivered to the block.
By following these steps and applying the relevant formulas, you should be able to calculate the answers to all three questions.