Josie and Charlotte push a 14-kg bag of playground sand for a sandbox on a frictionless, horizontal, wet polyvinyl surface with a constant, horizontal force for a distance of 8 m, starting from rest. If the final speed of the sand bag is 0.15 m/s, what is the magnitude of the force with which they pushed?
Fd = 1/2 mv^2
Plug. Chug.
To find the magnitude of the force with which Josie and Charlotte pushed the sandbag, 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 work done, W, is given by the equation:
W = ΔKE
where ΔKE is the change in kinetic energy. In this case, the initial kinetic energy of the sandbag is zero since it starts from rest. Therefore, the work done on the sandbag is equal to its final kinetic energy.
Let's calculate the work done:
KE = 0.5 * m * v^2
where m is the mass of the sandbag and v is its final velocity.
KE = 0.5 * 14 kg * (0.15 m/s)^2
KE = 0.5 * 14 kg * 0.0225 m^2/s^2
KE = 0.1575 J
Now we know that the work done, W, is equal to 0.1575 J.
According to the equation for work, W = F * d * cosθ, where F is the magnitude of the force, d is the distance, and θ is the angle between the force and the direction of displacement.
In this case, θ is 0 degrees because the force is horizontal and parallel to the displacement.
Therefore, the equation for work becomes:
W = F * d
Solving for F, we get:
F = W / d
F = 0.1575 J / 8 m
F = 0.0197 N
Therefore, the magnitude of the force with which Josie and Charlotte pushed the sandbag is approximately 0.0197 N.
To find the magnitude of the force with which Josie and Charlotte pushed the sandbag, we can use Newton's second law of motion, which states that the force of an object is equal to its mass multiplied by its acceleration.
In this case, we are given the mass of the sandbag, which is 14 kg, and the distance it travels, which is 8 m. We are also given the final speed of the sandbag, which is 0.15 m/s.
First, let's calculate the acceleration of the sandbag. We can use the formula:
v^2 = u^2 + 2as
Where:
- v is the final velocity (0.15 m/s)
- u is the initial velocity (which is 0 since it starts from rest)
- a is the acceleration
- s is the distance (8 m)
Rearranging the formula to solve for acceleration (a), we get:
a = (v^2 - u^2) / 2s
Plugging in the given values, we have:
a = (0.15^2 - 0^2) / (2 * 8)
a = 0.0225 / 16
a = 0.00140625 m/s^2
Now that we have the acceleration, we can find the force using Newton's second law. The formula is:
F = ma
Where:
- F is the force
- m is the mass (14 kg)
- a is the acceleration (0.00140625 m/s^2)
Plugging in the values, we have:
F = 14 kg * 0.00140625 m/s^2
F = 0.0196875 N
Therefore, the magnitude of the force with which Josie and Charlotte pushed the sandbag is approximately 0.0197 Newtons.