A 20.0 kg block is being pushed forward on a flat surface with a force of magnitude 45.0 N against a frictional force of 13.0 N.
A. What is the net force acting on the block?
B. What is the change in kinetic energy after the force has pushed the block for 4.0 m?
C. How much work would it take to stop the block?
A. 45 - 13 = 32 Newtons
B. Work done = 32 * 4 = 128 Newton meters or JOULES
C. -128 Joules total but the friction will do 13* 4 = 52 Joules so you need to absorb 128 - 52 if you stop it in 4 meters. Question C is not clear.
A. The net force acting on the block can be calculated by subtracting the frictional force from the applied force. So, the net force is:
Net Force = Applied Force - Frictional Force
Net Force = 45.0 N - 13.0 N
Net Force = 32.0 N
Therefore, the net force acting on the block is 32.0 N.
B. The change in kinetic energy can be calculated using the work-energy theorem. The work done on an object is equal to the change in kinetic energy. The equation for work is:
Work = Force × Distance × cos(θ)
Since the force and the displacement are in the same direction, the angle between them is 0°, so the cosine of the angle is 1. Therefore, the equation simplifies to:
Work = Force × Distance
The work done on the block is:
Work = Net Force × Distance
Work = 32.0 N × 4.0 m
Work = 128.0 J
This means that the force has done 128.0 Joules of work on the block.
C. The work done to stop the block completely would be equal to the initial kinetic energy of the block. The initial kinetic energy can be calculated using the equation:
Kinetic Energy = (1/2) × mass × velocity^2
Since the block is initially at rest, the initial velocity is 0 m/s. Therefore, the initial kinetic energy is 0 J.
So, it would take 0 Joules of work to stop the block completely.
To find the answers to these questions, we need to use some key formulas from physics.
A. The net force acting on an object is the vector sum of all the forces acting on it. In this case, we have two forces: the pushing force and the frictional force. Since the pushing force is in the forward direction and the frictional force opposes the motion, we subtract the frictional force from the pushing force to find the net force.
Net force = Pushing force - Frictional force
Net force = 45.0 N - 13.0 N
Net force = 32.0 N
So, the net force acting on the block is 32.0 N.
B. The change in kinetic energy of an object can be calculated using the work-energy principle. According to this principle, the work done on an object equals its change in kinetic energy.
The work done on an object is given by the formula:
Work = Force * Distance * cos(theta)
In this case, the force is the net force acting on the block, and the distance is the distance the block has been pushed (4.0 m). The angle theta is the angle between the force and displacement, which is 0 degrees since the force and displacement are in the same direction.
Work = Net force * Distance * cos(0)
Work = 32.0 N * 4.0 m * cos(0)
Work = 128.0 J
So, the change in kinetic energy after the force has pushed the block for 4.0 m is 128.0 J.
C. To calculate the work required to stop the block, we need to overcome its kinetic energy. The kinetic energy of an object can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity^2
Since the block is pushed, it will have some initial velocity. However, the question doesn't provide information about the initial velocity. Therefore, we can't find the exact work required to stop the block in this scenario without additional information.
However, if we assume the block is initially at rest (meaning its initial velocity is zero), then its initial kinetic energy would be zero.
Therefore, the work required to stop the block is equal to its initial kinetic energy, which is zero.
So, the work required to stop the block would be zero, assuming the block is initially at rest.