A little red wagon with mass 7.0kg moves in a straight line on a frictionless horizontal surface. It has an initial speed of4.00 m/s and then is pushed 3.0m in the direction of the initial velocity by a force with a magnitude of 10.0 N a.) Use the work-energy theorem to calculate the wagon's final speed b.) Calculate the acceleration produced by the force
Answer plz
To find the answers to these questions, we need to apply the work-energy theorem.
a.) The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.
Net work is calculated using the formula:
Net work = force * displacement * cos(theta)
In this case, the force is 10.0 N and the displacement is 3.0 m. As the force and displacement are in the same direction, the angle between them is 0 degrees, so cos(theta) = 1.
Therefore, the net work done on the wagon is:
Net work = 10.0 N * 3.0 m * 1 = 30 J (Joules)
The change in kinetic energy is given by:
Change in kinetic energy = final kinetic energy - initial kinetic energy
Since the wagon starts from rest, the initial kinetic energy is zero.
According to the work-energy theorem, net work is equal to the change in kinetic energy. Therefore:
30 J = final kinetic energy - 0
final kinetic energy = 30 J
The final speed is related to the final kinetic energy through the equation:
final kinetic energy = (1/2) * mass * (final speed)^2
Re-arranging the equation, we get:
(final speed)^2 = (2 * final kinetic energy) / mass
(final speed)^2 = (2 * 30 J) / 7.0 kg
(final speed)^2 = 60 J / 7.0 kg
(final speed)^2 = 8.57 m^2/s^2
final speed = sqrt(8.57) m/s
Therefore, the wagon's final speed is approximately 2.93 m/s.
b.) To calculate the acceleration produced by the force, 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.
In this case, the force is given as 10.0 N, and the mass of the wagon is 7.0 kg.
Therefore:
Net force = 10.0 N
Mass = 7.0 kg
Using Newton's second law:
Net force = Mass * Acceleration
10.0 N = 7.0 kg * Acceleration
Re-arranging the equation to solve for acceleration:
Acceleration = Net force / Mass
Acceleration = 10.0 N / 7.0 kg
Acceleration ≈ 1.43 m/s^2
Therefore, the acceleration produced by the force is approximately 1.43 m/s^2.